Rigid -dimensional compacta whose squares are manifolds

Authors:
Fredric D. Ancel, Paul F. Duvall and S. Singh

Journal:
Proc. Amer. Math. Soc. **88** (1983), 330-332

MSC:
Primary 54G20; Secondary 54B15, 55M15, 57P99

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695269-2

MathSciNet review:
695269

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A space is *rigid* if its only self-homeomorphism is the identity. In response to a question of Jan van Mill, Ancel and Singh have given examples of rigid -dimensional compacta, for each , whose squares are manifolds. We construct a rigid -dimensional compactum whose square is the manifold . In fact, we construct uncountably many topologically distinct compacta with these properties.

**[1]**F. D. Ancel and S. Singh,*Rigid finite dimensional compacta whose squares are manifolds*, Proc. Amer. Math. Soc.**87**(1982), 342-346. MR**681845 (83m:54074)****[2]**A. V. Arhangel'skii,*Structures and classification of topological spaces and cardinal invariants*, Russian Math. Surveys**33**(1978), 33-96. MR**526012 (80i:54005)****[3]**C. D. Bass,*Some products of topological spaces are manifolds*, Proc. Amer. Math. Soc.**81**(1981), 641-646. MR**601746 (82a:57012)****[4]**E. M. Brown,*Contractible**-manifolds of finite genus at infinity*, Trans. Amer. Math. Soc.**245**(1978), 503-514. MR**511426 (80g:57011)****[5]**R. C. Lacher,*Cell-like mappings and their generalizations*, Bull. Amer. Math. Soc.**83**(1977), 495-552. MR**0645403 (58:31095)****[6]**D. R. McMillan, Jr.,*Some contractible open**-manifolds*, Trans. Amer. Math. Soc.**102**(1962), 373-382. MR**0137105 (25:561)****[7]**J. van Mill,*A rigid space**for which**is homogeneous; an application of infinite dimensional topology*, Proc. Amer. Math. Soc.**83**(1981), 597-600. MR**627701 (82h:54067)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54G20,
54B15,
55M15,
57P99

Retrieve articles in all journals with MSC: 54G20, 54B15, 55M15, 57P99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695269-2

Keywords:
Cell-like compactum,
homogeneous,
manifold,
generalized -manifold,
cell-like decomposition

Article copyright:
© Copyright 1983
American Mathematical Society