메뉴 건너뛰기




Volumn 22, Issue 2, 2003, Pages 179-208

Selection principles in mathematics: A milestone of open problems

Author keywords

Arkhangel'ski property; Galvin Miller strong property; Gerlits Nagy property; Gerlits Nagy (*) property; Hurewicz property; Infinite game theory; Menger property; Ramsey theory; Rothberger property; Sakai property; Selection principles

Indexed keywords


EID: 33644783515     PISSN: 11232536     EISSN: 15900932     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (60)
  • 1
    • 0039109738 scopus 로고
    • Hurewicz spaces, analytic sets and fan tightness of function spaces
    • A. V. Arkhangel'skiǐ: Hurewicz spaces, analytic sets and fan tightness of function spaces, Soviet Mathematical Doklady 33 (1986), 396-399.
    • (1986) Soviet Mathematical Doklady , vol.33 , pp. 396-399
    • Arkhangel'skiǐ, A.V.1
  • 4
    • 0003858275 scopus 로고
    • Set Theory: On the structure of the real line
    • A. K. Peters, Massachusetts
    • T. Bartoszyński, H. Judah: Set Theory: On the structure of the real line, A. K. Peters, Massachusetts: 1995.
    • (1995)
    • Bartoszyński, T.1    Judah, H.2
  • 5
    • 0346331554 scopus 로고    scopus 로고
    • Additivity properties of topological diagonalizations
    • Full version
    • T. Bartoszyński, S. Shelah, B. Tsaban: Additivity properties of topological diagonalizations, Journal of Symbolic Logic, 68, (2003), 1254-1260. (Full version: http://arxiv.org/abs/math.LO/0112262)
    • (2003) Journal of Symbolic Logic , vol.68 , pp. 1254-1260
    • Bartoszyński, T.1    Shelah, S.2    Tsaban, B.3
  • 6
    • 3543102945 scopus 로고    scopus 로고
    • Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures
    • Proceedings of the American Mathematical Society, to appear
    • T. Bartoszyński, B. Tsaban: Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures, Proceedings of the American Mathematical Society, to appear. http://arxiv.org/abs/math.LO/0208224
    • Bartoszyński, T.1    Tsaban, B.2
  • 7
    • 0002059526 scopus 로고    scopus 로고
    • Ergodic Ramsey Theory - an update
    • in: Ergodic Theory of Zd-actions (ed. M. Pollicott and K. Schmidt)
    • V. Bergelson: Ergodic Ramsey Theory - an update, in: Ergodic Theory of Zd-actions (ed. M. Pollicott and K. Schmidt), London Math. Soc. Lecture Note Series 228 (1996), 1-61.
    • (1996) London Math. Soc. Lecture Note Series , vol.228 , pp. 1-61
    • Bergelson, V.1
  • 8
    • 0039717521 scopus 로고
    • Point-picking games and HFD's
    • in: Models and Sets, Proceedings of the Logic Colloquium 1983, Springer Verlag LNM
    • A. Berner, I. Juhašz: Point-picking games and HFD's, in: Models and Sets, Proceedings of the Logic Colloquium 1983, Springer Verlag LNM 1103 (1984), 53-66.
    • (1984) , vol.1103 , pp. 53-66
    • Berner, A.1    Juhašz, I.2
  • 9
    • 77649223767 scopus 로고    scopus 로고
    • Combinatorial cardinal characteristics of the continuum
    • in: Handbook of Set Theory (eds. Foreman, Kanamori, and Magidor), to appear
    • A. R. Blass: Combinatorial cardinal characteristics of the continuum, in: Handbook of Set Theory (eds. Foreman, Kanamori, and Magidor), to appear.
    • Blass, A.R.1
  • 10
    • 0003166916 scopus 로고    scopus 로고
    • Generic constructions of small sets of reals
    • J. Brendle: Generic constructions of small sets of reals, Topology and it Applications 71 (1996), 125-147.
    • (1996) Topology and it Applications , vol.71 , pp. 125-147
    • Brendle, J.1
  • 11
    • 15944390090 scopus 로고
    • Quasinormal convergence
    • Z. Bukovská: Quasinormal convergence, Math. Slovaca 41 (1991), 137-146.
    • (1991) Math. Slovaca , vol.41 , pp. 137-146
    • Bukovská, Z.1
  • 12
    • 48549097563 scopus 로고    scopus 로고
    • Not distinguishing convergences: Open problems
    • L. Bukovský: Not distinguishing convergences: Open problems, SPM Bulletin 3, 2-3.
    • SPM Bulletin , vol.3 , pp. 2-3
    • Bukovský, L.1
  • 13
    • 0037836186 scopus 로고
    • Spaces not distinguishing pointwise and quasinormal convergence of real functions
    • L. Bukovský, I. Reław, M. Repický: Spaces not distinguishing pointwise and quasinormal convergence of real functions, Topology and its Applications 41 (1991), 25-40.
    • (1991) Topology and its Applications , vol.41 , pp. 25-40
    • Bukovský, L.1    Reław, I.2    Repický, M.3
  • 14
    • 84887241916 scopus 로고    scopus 로고
    • On Hurewicz Properties
    • preprint
    • L. Bukovský, J. Haleš: On Hurewicz Properties, preprint.
    • Bukovský, L.1    Haleš, J.2
  • 15
    • 0002920988 scopus 로고
    • The integers and topology
    • in: Handbook of Set Theoretic Topology (eds. K. Kunen and J. Vaughan), North-Holland, Amsterdam
    • E. K. van Douwen: The integers and topology, in: Handbook of Set Theoretic Topology (eds. K. Kunen and J. Vaughan), North-Holland, Amsterdam: 1984, 111-167.
    • (1984) , pp. 111-167
    • Van Douwen, E.K.1
  • 17
    • 84882885402 scopus 로고    scopus 로고
    • SSP and WQN
    • preprint
    • D. H. Fremlin: SSP and WQN, preprint.
    • Fremlin, D.H.1
  • 18
    • 0001740764 scopus 로고
    • γ-sets and other singular sets of real numbers
    • F. Galvin, A. W. Miller γ-sets and other singular sets of real numbers, Topology and it Applications 17 (1984), 145-155.
    • (1984) Topology and it Applications , vol.17 , pp. 145-155
    • Galvin, F.1    Miller, A.W.2
  • 19
    • 84887237202 scopus 로고    scopus 로고
    • S. García-Ferreira, W. Just: Some remarks on the γp property, Questions and Answers in General Topology 17 (1999), 1-8.
    • García-Ferreira, S.1    Just, W.2
  • 23
    • 0038173867 scopus 로고
    • Über Folgen stetiger Funktionen
    • W. Hurewicz: Über Folgen stetiger Funktionen, Fundamenta Mathematicae 9 (1927), 193-204.
    • (1927) Fundamenta Mathematicae , vol.9 , pp. 193-204
    • Hurewicz, W.1
  • 24
    • 0001729944 scopus 로고    scopus 로고
    • The combinatorics of open covers II
    • W. Just, A. W. Miller, M. Scheepers, P. J. Szeptycki: The combinatorics of open covers II, Topology and its Applications 73 (1996), 241-266.
    • (1996) , vol.73 , pp. 241-266
    • Just, W.1    Miller, A.W.2    Scheepers, M.3    Szeptycki, P.J.4
  • 25
    • 33645912460 scopus 로고
    • On a theorem of A. H. Stone
    • A. P. Kombarov: On a theorem of A. H. Stone, Soveit Math. Dokl. 27 (1983), 544-547.
    • (1983) Soveit Math. Dokl. , vol.27 , pp. 544-547
    • Kombarov, A.P.1
  • 27
    • 84887219912 scopus 로고    scopus 로고
    • Combinatorics of open covers (VII): groupability
    • Fundamenta Mathematicae, to appear
    • Lj. D. R. Kočinac, M. Scheepers: Combinatorics of open covers (VII): groupability, Fundamenta Mathematicae, to appear.
    • Kočinac, L.J.D.R.1    Scheepers, M.2
  • 29
    • 0038631381 scopus 로고
    • On the length of Borel hierarchies
    • A. W. Miller: On the length of Borel hierarchies, Annals of Mathematical Logic 16 (1979), 233-267.
    • (1979) Annals of Mathematical Logic , vol.16 , pp. 233-267
    • Miller, A.W.1
  • 30
    • 0000654802 scopus 로고
    • Special subsets of the real line
    • in: Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam
    • A. W. Miller: Special subsets of the real line, in: Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North Holland, Amsterdam: 1984, 201-233.
    • (1984) , pp. 201-233
    • Miller, A.W.1
  • 31
    • 84887231300 scopus 로고    scopus 로고
    • A Nonhereditary Borel-cover γ-set
    • preprint
    • A. W. Miller: A Nonhereditary Borel-cover γ-set, preprint.
    • Miller, A.W.1
  • 32
    • 0032364277 scopus 로고    scopus 로고
    • The algebraic sum of sets of real numbers with strong measure zero sets
    • A. Nowik, M. Scheepers, T. Weiss: The algebraic sum of sets of real numbers with strong measure zero sets, J. Symbolic Logic 63 (1998), 301-324.
    • (1998) J. Symbolic Logic , vol.63 , pp. 301-324
    • Nowik, A.1    Scheepers, M.2    Weiss, T.3
  • 33
    • 0009886960 scopus 로고
    • Parametrized Cichoń's diagram and small sets
    • J. Pawlikowski, I. Recław: Parametrized Cichoń's diagram and small sets, Fundamenta Mathematicae 147 (1995), 135-155.
    • (1995) Fundamenta Mathematicae , vol.147 , pp. 135-155
    • Pawlikowski, J.1    Reław, I.2
  • 34
    • 0011555625 scopus 로고
    • Every Luzin set is undetermined in point-open game
    • I. Rec law: Every Luzin set is undetermined in point-open game, Fundamenta Mathematicae 144 (1994), 43-54.
    • (1994) Fundamenta Mathematicae , vol.144 , pp. 43-54
    • Reław, I.1
  • 36
    • 3543059690 scopus 로고    scopus 로고
    • The Pytkeev property and the Reznichenko property in function spaces
    • Note di Matematica, to appear
    • M. Sakai: The Pytkeev property and the Reznichenko property in function spaces, Note di Matematica, to appear.
    • Sakai, M.1
  • 37
    • 0038173864 scopus 로고    scopus 로고
    • Combinatorics of open covers I: Ramsey Theory
    • M. Scheepers: Combinatorics of open covers I: Ramsey Theory, Topology and its Applications 69 (1996), 31-62.
    • (1996) Topology and its Applications , vol.69 , pp. 31-62
    • Scheepers, M.1
  • 38
    • 21944441297 scopus 로고    scopus 로고
    • A sequential property of Cp(X) and a covering property of Hurewicz
    • M. Scheepers: A sequential property of Cp(X) and a covering property of Hurewicz, Proceedings of the American Mathematical Society 125 (1997), 2789-2795.
    • (1997) Proceedings of the American Mathematical Society , vol.125 , pp. 2789-2795
    • Scheepers, M.1
  • 39
    • 0040715545 scopus 로고    scopus 로고
    • Combinatorics of open covers (IV): subspaces of the Alexandró double of the unit interval
    • M. Scheepers: Combinatorics of open covers (IV): subspaces of the Alexandró double of the unit interval, Topology and its Applications 83 (1998), 63-75.
    • (1998) Topology and its Applications , vol.83 , pp. 63-75
    • Scheepers, M.1
  • 41
    • 0037836180 scopus 로고    scopus 로고
    • Sequential convergence in Cp(X) and a covering property
    • M. Scheepers: Sequential convergence in Cp(X) and a covering property, East-West Journal of Mathematics 1 (1999), 207-214.
    • (1999) East-West Journal of Mathematics , vol.1 , pp. 207-214
    • Scheepers, M.1
  • 42
    • 0033484417 scopus 로고    scopus 로고
    • The length of some diagonalization games
    • M. Scheepers: The length of some diagonalization games, Arch. Math. Logic 38 (1999), 103-122.
    • (1999) Arch. Math. Logic , vol.38 , pp. 103-122
    • Scheepers, M.1
  • 43
    • 1942491144 scopus 로고    scopus 로고
    • Combinatorics of open covers (V): Pixley-Roy spaces and sets of reals, and omega-covers
    • M. Scheepers: Combinatorics of open covers (V): Pixley-Roy spaces and sets of reals, and omega-covers, Topology and its Applications 102 (2000), 13-31.
    • (2000) Topology and its Applications , vol.102 , pp. 13-31
    • Scheepers, M.1
  • 44
    • 84887256865 scopus 로고    scopus 로고
    • Combinatorics of open covers (VI): Selectors for sequences of dense sets
    • Quaestiones Mathematicae, to appear
    • M. Scheepers: Combinatorics of open covers (VI): Selectors for sequences of dense sets, Quaestiones Mathematicae, to appear.
    • Scheepers, M.1
  • 45
    • 84887254611 scopus 로고    scopus 로고
    • Cp(X) and Arkhangel'skiǐ's ǐ spaces
    • Topology and its Applications, to appear
    • M. Scheepers: Cp(X) and Arkhangel'skiǐ's ǐ spaces, Topology and its Applications, to appear.
    • Scheepers, M.1
  • 46
    • 84887214126 scopus 로고    scopus 로고
    • Open covers and the square bracket partition relation
    • preprint
    • M. Scheepers: Open covers and the square bracket partition relation, preprint.
    • Scheepers, M.1
  • 47
    • 0038351767 scopus 로고    scopus 로고
    • The combinatorics of Borel covers
    • M. Scheepers, B. Tsaban: The combinatorics of Borel covers, Topology and its Applications 121 (2002), 357-382. http://arxiv.org/abs/math.GN/0302322
    • (2002) Topology and its Applications , vol.121 , pp. 357-382
    • Scheepers, M.1    Tsaban, B.2
  • 48
    • 84887234766 scopus 로고    scopus 로고
    • Selection principles and covering properties in topology
    • Note di Matematica, this volume
    • M. Scheepers: Selection principles and covering properties in topology, Note di Matematica, this volume.
    • Scheepers, M.1
  • 49
    • 3543122719 scopus 로고    scopus 로고
    • Critical cardinalities and additivity properties of combinatorial notions of smallness
    • S. Shelah, B. Tsaban: Critical cardinalities and additivity properties of combinatorial notions of smallness, Journal of Applied Analysis 9 (2003), 149-162. http://arxiv.org/abs/math.LO/0304019
    • (2003) Journal of Applied Analysis , vol.9 , pp. 149-162
    • Shelah, S.1    Tsaban, B.2
  • 51
    • 0037818919 scopus 로고    scopus 로고
    • A topological interpretation of t
    • B. Tsaban: A topological interpretation of t, Real Analysis Exchange 25 (1999/2000), 391-404. http://arxiv.org/abs/math.LO/9705209
    • (1999) Real Analysis Exchange , vol.25 , pp. 391-404
    • Tsaban, B.1
  • 52
    • 84887242503 scopus 로고    scopus 로고
    • SPM Bulletin, January
    • B. Tsaban (ed.), SPM Bulletin 1 (January 2003), http://arxiv.org/abs/math.GN/0301011
    • (2003) , pp. 1
    • Tsaban, B.1
  • 53
    • 84887227001 scopus 로고    scopus 로고
    • SPM Bulletin, February
    • B. Tsaban (ed.), SPM Bulletin 2 (February 2003), http://arxiv.org/abs/math.GN/0302062
    • (2003) , pp. 2
    • Tsaban, B.1
  • 54
    • 84887238566 scopus 로고    scopus 로고
    • SPM Bulletin,March
    • B. Tsaban (ed.), SPM Bulletin 3 (March 2003), http://arxiv.org/abs/math.GN/0303057
    • (2003) , pp. 3
    • Tsaban, B.1
  • 55
    • 84887228983 scopus 로고    scopus 로고
    • SPM Bulletin, April
    • B. Tsaban (ed.), SPM Bulletin 4 (April 2003), http://arxiv.org/abs/math.GN/0304087
    • (2003) , pp. 4
    • Tsaban, B.1
  • 56
    • 84887233303 scopus 로고    scopus 로고
    • SPM Bulletin, SPEC. ISSUE, May
    • B. Tsaban (ed.), SPM Bulletin 5 - special issue (May 2003), http://arxiv.org/abs/math.GN/0305367
    • (2003) , pp. 5
    • Tsaban, B.1
  • 57
    • 84887234087 scopus 로고    scopus 로고
    • SPM Bulletin, November
    • B. Tsaban (ed.), SPM Bulletin 6 (November 2003), http://arxiv.org/abs/math.GN/0312140
    • (2003) , pp. 6
    • Tsaban, B.1
  • 58
    • 3543091537 scopus 로고    scopus 로고
    • The combinatorics of splittability
    • B. Tsaban: The combinatorics of splittability, Annals of Pure and Applied Logic, 129, (2004), 107-130.
    • (2004) Annals of Pure and Applied Logic , vol.129 , pp. 107-130
    • Tsaban, B.1
  • 59
    • 3543116965 scopus 로고    scopus 로고
    • Selection principles and the minimal tower problem
    • Note di Matematica, this volume
    • B. Tsaban: Selection principles and the minimal tower problem, Note di Matematica, this volume. http://arxiv.org/abs/math.LO/0105045
    • Tsaban, B.1
  • 60
    • 2442691691 scopus 로고    scopus 로고
    • The minimal cardinality where the Reznichenko property fails
    • B. Tsaban: The minimal cardinality where the Reznichenko property fails, Israel Journal of Mathematics, 140, (2004), 367-374.
    • (2004) Israel Journal of Mathematics , vol.140 , pp. 367-374
    • Tsaban, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.