Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An AR-map whose range is more infinite-dimensional than its domain


Authors: J. J. Dijkstra, J. van Mill and J. Mogilski
Journal: Proc. Amer. Math. Soc. 114 (1992), 279-285
MSC: Primary 54C55; Secondary 54G20, 57N20
DOI: https://doi.org/10.1090/S0002-9939-1992-1075946-X
MathSciNet review: 1075946
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct an example of an AR-map $ f:X \to Y$, where $ X$ is a strongly countable dimensional compact AR and $ Y$ is a countable dimensional AR which is not strongly countable dimensional. Using this map we find a shrinkable decomposition of the pre-Hilbert space $ l_f^2$ whose quotient map does not stabilize to a near homeomorphism. We also present a partial result concerning the question whether cell-like maps preserve countable dimensionality.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C55, 54G20, 57N20

Retrieve articles in all journals with MSC: 54C55, 54G20, 57N20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1075946-X
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society