Homeomorphism groups of manifolds and erdŐs space

Electronic Research Announcements of the American Mathematical Society

Volumn 10, Issue 4, 2004, Pages 29-38

  Dijkstra, Jan J ^a   Van Mill, Jan ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

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[No Author keywords available]

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EID: 15944420942     PISSN: None     EISSN: 10796762     Source Type: Journal    
DOI: 10.1090/S1079-6762-04-00127-1     Document Type: Article

References (30)

1. S. Ageev, A characterization of k-dimensional Nöbeling space for every k 1, 2002 preprint.
2. R. D. Anderson, Spaces of homeomorphisms of finite graphs, unpublished manuscript.
3. R. Arens, Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593-610. MR 8:479i
4. C. Bessaga and A. Pe lczyński, Selected topics in infinite-dimensional topology, Mathematical Monographs, Vol. 58, PWN Polish Scientific Publishers, Warsaw, 1975. MR 57:17657
5. M. Bestvina, Characterizing k-dimensional universal Menger compacta, Mem. Amer.Math. Soc. 71 (1988), no. 380. MR 89g:54083
6. L. E. J. Brouwer, On the structure of perfect sets of points, Proc. Akad. Amsterdam 12 (1910), 785-794.
7. L. E. J. Brouwer, Some remarks on the coherence type n, Proc. Akad. Amsterdam 15 (1913), 1256-1263.
8. W. D. Bula and L. G. Oversteegen, A characterization of smooth Cantor bouquets, Proc. Amer. Math. Soc. 108 (1990), 529-534. MR 90d:54066
9. W. J. Charatonik, The Lelek fan is unique, Houston J. Math. 15 (1989), 27-34. MR 90f:54050
10. J. J. Dijkstra, On homeomorphism groups of Menger continua, 2003 preprint.
11. J. J. Dijkstra, On homeomorphism groups and the compact-open topology, 2003 preprint.
12. J. J. Dijkstra and J. van Mill, On the group of homeomorphisms of the real line that map the pseudoboundary onto itself, 2002 preprint.
13. J. J. Dijkstra and J. van Mill, Erdős space and homeomorphism groups of manifolds, in preparation.
14. J. J. Dijkstra, J. van Mill, and J. Steprāns, Complete Erdős space is unstable, Math. Proc. Cambridge Philos. Soc., to appear.
15. T. Dobrowolski and H. Toruńczyk, Separable complete ANRs admitting a group structure are Hilbert manifolds, Topology Appl. 12 (1981), 229-235. MR 83a:58007
16. A. J. M. van Engelen, Homogeneous zero-dimensional absolute Borel sets, CWI Tract, Vol. 27, Centre for Mathematics and Computer Science, Amsterdam, 1986. MR 87j:54058
17. P. Erdős, The dimension of the rational points in Hilbert space, Ann. of Math. 41 (1940), 734-736. MR 2:178a
18. S. Ferry, The homeomorphism group of a compact Hilbert cube manifold is an ANR, Ann. of Math. 106 (1977), 101-119. MR 57:1521
19. K. Kawamura, L. G. Oversteegen, and E. D. Tymchatyn, On homogeneous totally disconnected 1-dimensional spaces, Fund. Math. 150 (1996), 97-112. MR 97d:54060
20. J. E. Keesling, Using ows to construct Hilbert space factors of function spaces, Trans. Amer. Math. Soc. 161 (1971), 1-24. MR 44:981
21. A. Lelek, On plane dendroids and their end points in the classical sense, Fund. Math. 49 (1961), 301-319. MR 24:A363
22. M. Levin and R. Pol, A metric condition which implies dimension ≤1, Proc. Amer. Math. Soc. 125 (1997), 269-273. MR 97e:54033
23. R. Luke and W. K. Mason, The space of homeomorphisms of a compact two-manifold is an Absolute Neighborhood Retract, Trans. Amer. Math. Soc. 164 (1972), 275-285. MR 46:849
24. L. G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994), 885-891. MR 95b:54040
25. R. Pol, There is no universal totally disconnected space, Fund. Math. 70 (1973), 265-267. MR 48:1139
26. σδ, Fund. Math. 6 (1924), 24-29.
27. J. R. Steel, Analytic sets and Borel isomorphisms, Fund. Math. 108 (1980), 83-88. MR 82b:03091
28. H. Toruńczyk, Homeomorphism groups of compact Hilbert cube manifolds which are manifolds, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 401-408. MR 58:24302
29. H. Toruńczyk, On CE-images of the Hilbert cube and characterizations of Q-manifolds, Fund. Math. 106 (1980), 31-40. MR 83g:57006
30. H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), 247-262. MR 82i:57016