An AR-map whose range is more infinite-dimensional than its domain
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- by J. J. Dijkstra, J. van Mill and J. Mogilski PDF
- Proc. Amer. Math. Soc. 114 (1992), 279-285 Request permission
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
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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