Proper hereditary shape equivalences preserve small weak infinite-dimensionality

Author:
Richard P. Millspaugh

Journal:
Proc. Amer. Math. Soc. **110** (1990), 1055-1061

MSC:
Primary 54F45; Secondary 54C10

DOI:
https://doi.org/10.1090/S0002-9939-1990-1037215-1

MathSciNet review:
1037215

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A space is said to be small weakly infinite dimensional if it has a basis such that the collection of finite unions of elements of is inessential. A characterization of small weak infinite dimensionality is given for locally compact spaces. This characterization is then used to prove that if is a proper hereditary shape equivalence from a metric space which is small weakly infinite dimensional onto a locally compact metric space , then is small weakly infinite dimensional.

**[AG]**D. F. Addis and J. H. Gresham,*A class of infinite dimensional spaces, Part*I:*Dimension theory and Alexandroff's problem*, Fund. Math.**101**(1978), 195-205. MR**521122 (80b:54041)****[A1]**F. D. Ancel,*Proper hereditary shape equivalences preserve property*, Topology Appl.**19**(1985), 71-74. MR**786082 (86g:54026)****[A2]**-,*The role of countable dimensionality in the theory of cell-like relations*, Trans. Amer. Math. Soc.**287**(1985), 1-40. MR**766204 (86b:54012)****[B1]**P. Borst,*Spaces having a weakly-infinite-dimensional compactification*, Topology Appl.**21**(1985), 261-268. MR**812644 (87g:54078)****[B2]**-,*Some remarks concerning**-spaces*, preprint.**[H]**S. T. Hu,*Theory of retracts*, Wayne State University Press, Detroit, 1965. MR**0181977 (31:6202)****[HW]**W. Hurewicz and H. Wallman,*Dimension theory*, Princeton University Press, Princeton, NJ, 1941. MR**0006493 (3:312b)****[R]**D. Rohm,*Hereditary shape equivalences preserve weak infinite dimensionality*, preprint.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54F45,
54C10

Retrieve articles in all journals with MSC: 54F45, 54C10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1037215-1

Keywords:
Small weakly infinite dimensional,
hereditary shape equivalence,
approximately invertible map,
inessential

Article copyright:
© Copyright 1990
American Mathematical Society