On homeomorphism groups of Menger continua

Transactions of the American Mathematical Society

Volumn 357, Issue 7, 2005, Pages 2665-2679

  Dijkstra, Jan J ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Complete Erdo s space; Homeomorphism group; Menger continuum; Sierpi ski carpet; Topological dimension

Indexed keywords

EID: 22544488374     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03863-8     Document Type: Article

References (18)

1. R. D. Anderson, A characterization of the universal curve and a proof of its homogeneity, Ann. of Math. 67 (1958), 313-324. MR0096180 (20:2675)
2. R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. 68 (1958), 1-16. MR0096181 (20:2676)
3. R. Arens, Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593-610. MR0019916 (8:479i)
4. M. Bestvina, Characterizing k-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 71 (1988), no. 380, vi+110. MR0920964 (89g:54083)
5. B. L. Brechner, On the dimensions of certain spaces of homeomorphisms, Trans. Amer. Math. Soc. 121 (1966), 516-548. MR0187208 (32:4662)
6. B. L. Brechner, Questions on homeomorphism groups of chainable and homogeneous continua, Topology Proc. 7 (1982), 391-393.
7. n (n ≠ 4), Fund. Math. 79 (1973), no. 2, 107-112. MR0319203 (47:7748)
8. J. J. Dijkstra, On homeomorphism groups and the compact-open topology, Amer. Math. Monthly, to appear.
9. J. J. Dijkstra, A criterion for Erdo″s spaces, Proc. Edinburgh Math. Soc., to appear.
10. J. J. Dijkstra and J. van Mill, Homeomorphism groups of manifolds and Erdo″s space, Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 29-38. MR2048429
11. J. J. Dijkstra and J. van Mill, On the group of homeomorphisms of the real line that map the pseudoboundary onto itself, preprint.
12. J. J. Dijkstra and J. van Mill, Erdo″s space and homeomorphism groups of manifolds, preprint.
13. J. J. Dijkstra, J. van Mill, and J. Steprāns, Complete Erdo″s space is unstable, Math. Proc. Cambridge Philos. Soc. 137 (2004), 465-473. MR2092071
14. R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978. MR0482697 (58:2753b)
15. P. Erdo″s, The dimension of the rational points in Hilbert space, Ann. of Math. 41 (1940), 734-736. MR0003191 (2:178a)
16. K. Kawamura, L. G. Oversteegen, and E. D. Tymchatyn, On homogeneous totally disconnected 1-dimensional spaces, Fund. Math. 150 (1996), 97-112. MR1391294 (97d:54060)
17. L. G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994), 885-891. MR1273515 (95b:54040)
18. G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320-324. MR0099638 (20:6077)