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Volumn 439, Issue , 2015, Pages 373-416

Dual closure operators and their applications

Author keywords

Cassidy H bert Kelly dual closure operator; Closure operator; Concordant map; Dual closure operator; Eilenberg Whyburn dual closure operator; Monotone map; Multi monocoreflective subcategory; Preradical

Indexed keywords


EID: 84936791600     PISSN: 00218693     EISSN: 1090266X     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2015.04.041     Document Type: Article
Times cited : (16)

References (53)
  • 2
    • 0343767742 scopus 로고
    • Connectedness and disconnectedness in topology
    • Arhangel'skii A., Wiegandt R. Connectedness and disconnectedness in topology. Topology Appl. 1975, 5:9-33.
    • (1975) Topology Appl. , vol.5 , pp. 9-33
    • Arhangel'skii, A.1    Wiegandt, R.2
  • 3
    • 34250559569 scopus 로고
    • Verallgemeinerung eines Faktorisierungssatzes von G. Whyburn
    • Bauer H. Verallgemeinerung eines Faktorisierungssatzes von G. Whyburn. Arch. Math. (Basel) 1959, 10:373-378.
    • (1959) Arch. Math. (Basel) , vol.10 , pp. 373-378
    • Bauer, H.1
  • 4
    • 25444437416 scopus 로고
    • Abschwächungen des Adjunktionsbegriffs
    • Börger R., Tholen W. Abschwächungen des Adjunktionsbegriffs. Manuscripta Math. 1976, 19:19-45.
    • (1976) Manuscripta Math. , vol.19 , pp. 19-45
    • Börger, R.1    Tholen, W.2
  • 5
    • 0009235172 scopus 로고
    • Concordant-dissonant and monotone-light
    • Heldermann Verlag, Berlin
    • Börger R., Tholen W. Concordant-dissonant and monotone-light. Categorical Topology 1984, 90-107. Heldermann Verlag, Berlin.
    • (1984) Categorical Topology , pp. 90-107
    • Börger, R.1    Tholen, W.2
  • 6
    • 33748750339 scopus 로고    scopus 로고
    • Torsion theories in homological categories
    • Bourn D., Gran M. Torsion theories in homological categories. J. Algebra 2006, 305:18-47.
    • (2006) J. Algebra , vol.305 , pp. 18-47
    • Bourn, D.1    Gran, M.2
  • 9
    • 80053203746 scopus 로고    scopus 로고
    • Interior operators in a category: idempotency and heredity
    • Castellini G. Interior operators in a category: idempotency and heredity. Topology Appl. 2011, 158:2332-2339.
    • (2011) Topology Appl. , vol.158 , pp. 2332-2339
    • Castellini, G.1
  • 10
    • 79955395017 scopus 로고    scopus 로고
    • Interior operators and topological connectedness
    • Castellini G., Ramos J. Interior operators and topological connectedness. Quaest. Math. 2010, 33:290-304.
    • (2010) Quaest. Math. , vol.33 , pp. 290-304
    • Castellini, G.1    Ramos, J.2
  • 11
    • 84974201299 scopus 로고
    • Reflective subcategories, localizations, and factorization systems
    • Cassidy C., Hébert M., Kelly G.M. Reflective subcategories, localizations, and factorization systems. J. Austral. Math. Soc., Ser. A 1985, 38:387-429.
    • (1985) J. Austral. Math. Soc., Ser. A , vol.38 , pp. 387-429
    • Cassidy, C.1    Hébert, M.2    Kelly, G.M.3
  • 12
    • 84936748070 scopus 로고
    • On connectedness and disconnectedness
    • János Bolyai Math. Soc., Budapest
    • Clementino M.M. On connectedness and disconnectedness. Topology with Applications 1995, 71-82. János Bolyai Math. Soc., Budapest.
    • (1995) Topology with Applications , pp. 71-82
    • Clementino, M.M.1
  • 13
    • 0035507378 scopus 로고    scopus 로고
    • On connectedness via closure operators
    • Clementino M.M. On connectedness via closure operators. Appl. Categ. Structures 2001, 9:539-556.
    • (2001) Appl. Categ. Structures , vol.9 , pp. 539-556
    • Clementino, M.M.1
  • 14
    • 33748699561 scopus 로고    scopus 로고
    • Torsion theories and radicals in normal categories
    • Clementino M.M., Dikranjan D., Tholen W. Torsion theories and radicals in normal categories. J. Algebra 2006, 305:98-129.
    • (2006) J. Algebra , vol.305 , pp. 98-129
    • Clementino, M.M.1    Dikranjan, D.2    Tholen, W.3
  • 15
    • 0041886195 scopus 로고    scopus 로고
    • Separation versus connectedness
    • Clementino M.M., Tholen W. Separation versus connectedness. Topology Appl. 1997, 75:143-181.
    • (1997) Topology Appl. , vol.75 , pp. 143-181
    • Clementino, M.M.1    Tholen, W.2
  • 17
    • 84968480760 scopus 로고
    • Concordant mappings and the concordant-dissonant factorization of an arbitrary continuous function
    • Collins P. Concordant mappings and the concordant-dissonant factorization of an arbitrary continuous function. Proc. Amer. Math. Soc. 1971, 27:587-591.
    • (1971) Proc. Amer. Math. Soc. , vol.27 , pp. 587-591
    • Collins, P.1
  • 19
    • 75849154761 scopus 로고    scopus 로고
    • Interior and closure operators on texture spaces-I: basic concepts and Čech closure operators
    • Diker M., Dost S., Altay Uğur A. Interior and closure operators on texture spaces-I: basic concepts and Čech closure operators. Fuzzy Sets and Systems 2010, 161:935-953.
    • (2010) Fuzzy Sets and Systems , vol.161 , pp. 935-953
    • Diker, M.1    Dost, S.2    Altay Uğur, A.3
  • 20
    • 75849144774 scopus 로고    scopus 로고
    • Interior and closure operators on texture spaces-II: Dikranjan-Giuli closure operators and Hutton algebras
    • Diker M., Dost S., Altay Uğur A. Interior and closure operators on texture spaces-II: Dikranjan-Giuli closure operators and Hutton algebras. Fuzzy Sets and Systems 2010, 161:954-972.
    • (2010) Fuzzy Sets and Systems , vol.161 , pp. 954-972
    • Diker, M.1    Dost, S.2    Altay Uğur, A.3
  • 23
    • 0037819490 scopus 로고
    • Categorical Structure of Closure Operators. With Applications to Topology, Algebra and Discrete Mathematics
    • Kluwer, Dordrecht
    • Dikranjan D., Tholen W. Categorical Structure of Closure Operators. With Applications to Topology, Algebra and Discrete Mathematics. Mathematics and Its Applications 1995, vol. 346. Kluwer, Dordrecht.
    • (1995) Mathematics and Its Applications , vol.346
    • Dikranjan, D.1    Tholen, W.2
  • 24
    • 33646003613 scopus 로고    scopus 로고
    • Classification of closure operators for categories of topological spaces
    • World Scientific, Singapore, W. Gähler, G. Preuss (Eds.)
    • Dikranjan D., Tholen W., Watson S. Classification of closure operators for categories of topological spaces. Categorical Structures and Their Applications 2004, 69-98. World Scientific, Singapore. W. Gähler, G. Preuss (Eds.).
    • (2004) Categorical Structures and Their Applications , pp. 69-98
    • Dikranjan, D.1    Tholen, W.2    Watson, S.3
  • 25
    • 84861460306 scopus 로고    scopus 로고
    • A description of the fundamental group in terms of commutators and closure operators
    • Duckerts M., Everaert T., Gran M. A description of the fundamental group in terms of commutators and closure operators. J. Pure Appl. Algebra 2012, 216:1837-1851.
    • (2012) J. Pure Appl. Algebra , vol.216 , pp. 1837-1851
    • Duckerts, M.1    Everaert, T.2    Gran, M.3
  • 26
    • 2542470000 scopus 로고
    • Categorical cuts
    • Dyckhoff R. Categorical cuts. Gen. Topol. Appl. 1976, 6:291-295.
    • (1976) Gen. Topol. Appl. , vol.6 , pp. 291-295
    • Dyckhoff, R.1
  • 27
    • 0010139675 scopus 로고
    • Sur les transformations continues d'espaces metriques compacts
    • Eilenberg S. Sur les transformations continues d'espaces metriques compacts. Fund. Math. 1934, 22:292-296.
    • (1934) Fund. Math. , vol.22 , pp. 292-296
    • Eilenberg, S.1
  • 28
    • 84888063473 scopus 로고    scopus 로고
    • Monotone-light factorization systems and torsion theories
    • Everaert T., Gran M. Monotone-light factorization systems and torsion theories. Bull. Sci. Math. 2013, 137:996-1006.
    • (2013) Bull. Sci. Math. , vol.137 , pp. 996-1006
    • Everaert, T.1    Gran, M.2
  • 29
    • 0043277401 scopus 로고
    • Topologische Reflexionen und Coreflexionen
    • Springer, Berlin
    • Herrlich H. Topologische Reflexionen und Coreflexionen. Lecture Notes in Math. 1968, vol. 78. Springer, Berlin.
    • (1968) Lecture Notes in Math. , vol.78
    • Herrlich, H.1
  • 31
    • 80053203083 scopus 로고    scopus 로고
    • Categorical neighborhood operators
    • Holgate D., Šlapal J. Categorical neighborhood operators. Topology Appl. 2011, 158:2356-2365.
    • (2011) Topology Appl. , vol.158 , pp. 2356-2365
    • Holgate, D.1    Šlapal, J.2
  • 32
    • 0001920057 scopus 로고
    • Epimorphisms and dominions
    • Springer, Berlin
    • Isbell J.R. Epimorphisms and dominions. Proc. Conf. Categorical Algebra 1966, 232-246. Springer, Berlin.
    • (1966) Proc. Conf. Categorical Algebra , pp. 232-246
    • Isbell, J.R.1
  • 34
    • 0033569279 scopus 로고    scopus 로고
    • Functorial factorization, well-pointedness and separability
    • Janelidze G., Tholen W. Functorial factorization, well-pointedness and separability. J. Pure Appl. Algebra 1999, 142:99-130.
    • (1999) J. Pure Appl. Algebra , vol.142 , pp. 99-130
    • Janelidze, G.1    Tholen, W.2
  • 35
    • 0010928038 scopus 로고
    • Locally adjunctable functors
    • Kaput J.J. Locally adjunctable functors. Illinois J. Math. 1972, 16:86-94.
    • (1972) Illinois J. Math. , vol.16 , pp. 86-94
    • Kaput, J.J.1
  • 36
    • 84971195724 scopus 로고
    • A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
    • Kelly G.M. A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on. Bull. Aust. Math. Soc. 1980, 22:1-83.
    • (1980) Bull. Aust. Math. Soc. , vol.22 , pp. 1-83
    • Kelly, G.M.1
  • 37
    • 84936749840 scopus 로고    scopus 로고
    • Interior operators and topological categories
    • Luna-Torres J., Ochoa C. Interior operators and topological categories. Adv. Appl. Math. Sci. 2011, 10:189-206.
    • (2011) Adv. Appl. Math. Sci. , vol.10 , pp. 189-206
    • Luna-Torres, J.1    Ochoa, C.2
  • 38
  • 39
    • 79951821437 scopus 로고
    • On continuous decomposition of bicompacts
    • Ponomarev V.I. On continuous decomposition of bicompacts. Usp. Math. Nauk 1957, 12:335-340.
    • (1957) Usp. Math. Nauk , vol.12 , pp. 335-340
    • Ponomarev, V.I.1
  • 40
    • 34250480411 scopus 로고
    • Trennung und Zusammenhang
    • Preuß G. Trennung und Zusammenhang. Monatsh. Math. 1970, 74:70-87.
    • (1970) Monatsh. Math. , vol.74 , pp. 70-87
    • Preuß, G.1
  • 41
    • 0041150876 scopus 로고
    • Eine Galoiskorrespondenz in der Topologie
    • Preuß G. Eine Galoiskorrespondenz in der Topologie. Monatsh. Math. 1971, 75:447-452.
    • (1971) Monatsh. Math. , vol.75 , pp. 447-452
    • Preuß, G.1
  • 42
    • 0011453195 scopus 로고
    • Reflective Subcategories and Closure Operators
    • Springer, Berlin
    • Salbany S. Reflective Subcategories and Closure Operators. Lecture Notes in Math. 1976, vol. 540:548-565. Springer, Berlin.
    • (1976) Lecture Notes in Math. , vol.540 , pp. 548-565
    • Salbany, S.1
  • 43
    • 84911628627 scopus 로고
    • Local Monocoreflectivity in Topological Categories
    • Springer, Berlin
    • Salicrup G. Local Monocoreflectivity in Topological Categories. Lecture Notes in Math. 1982, vol. 915:293-309. Springer, Berlin.
    • (1982) Lecture Notes in Math. , vol.915 , pp. 293-309
    • Salicrup, G.1
  • 45
    • 0041385266 scopus 로고
    • Connection and Disconnection
    • Springer, Berlin
    • Salicrup G., Vázquez R. Connection and Disconnection. Lecture Notes in Math. 1979, vol. 719:326-344. Springer, Berlin.
    • (1979) Lecture Notes in Math. , vol.719 , pp. 326-344
    • Salicrup, G.1    Vázquez, R.2
  • 46
    • 0010134358 scopus 로고
    • MacNeille completion of concrete categories with local properties
    • Tholen W. MacNeille completion of concrete categories with local properties. Comment. Math. Univ. St. Pauli 1979, 28:179-202.
    • (1979) Comment. Math. Univ. St. Pauli , vol.28 , pp. 179-202
    • Tholen, W.1
  • 47
    • 84909936366 scopus 로고
    • Factorizations, fibres and connectedness
    • Heldermann Verlag, Berlin
    • Tholen W. Factorizations, fibres and connectedness. Categorical Topology 1984, 549-566. Heldermann Verlag, Berlin.
    • (1984) Categorical Topology , pp. 549-566
    • Tholen, W.1
  • 49
    • 0141967770 scopus 로고    scopus 로고
    • Objects with dense diagonals
    • Kluwer, Dordrecht, E. Giuli (Ed.)
    • Tholen W. Objects with dense diagonals. Categorical Topology 1996, 213-220. Kluwer, Dordrecht. E. Giuli (Ed.).
    • (1996) Categorical Topology , pp. 213-220
    • Tholen, W.1
  • 50
    • 80053176415 scopus 로고    scopus 로고
    • Closure operators and their middle-interchange law
    • Tholen W. Closure operators and their middle-interchange law. Topology Appl. 2011, 158:2437-2441.
    • (2011) Topology Appl. , vol.158 , pp. 2437-2441
    • Tholen, W.1
  • 51
    • 79955418473 scopus 로고    scopus 로고
    • Interior operators in general categories
    • Vorster S.J.R. Interior operators in general categories. Quaest. Math. 2000, 23:405-416.
    • (2000) Quaest. Math. , vol.23 , pp. 405-416
    • Vorster, S.J.R.1
  • 52
    • 2542420258 scopus 로고
    • Non-alternating transformations
    • Whyburn G.T. Non-alternating transformations. Bull. Amer. Math. Soc. 1934, 56:294-302.
    • (1934) Bull. Amer. Math. Soc. , vol.56 , pp. 294-302
    • Whyburn, G.T.1
  • 53
    • 84913135403 scopus 로고
    • Open and closed mappings
    • Whyburn G.T. Open and closed mappings. Duke Math. J. 1950, 17:69-74.
    • (1950) Duke Math. J. , vol.17 , pp. 69-74
    • Whyburn, G.T.1


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