Atlas: On $C_\alpha$-Compact Subsets by Salvador Garcia-Ferreira

Atlas home || Conferences | Abstracts | about Atlas

The Eleventh Summer Conference on General Topology and Applications
August 10-13, 1995
University of Southern Maine
Gorham, ME, USA

Organizers
J. Baumgartner, D. Briggs, J. deBakker, B. Flagg, G. Gruenhage, M. Guay, Y. Kong, R. Kopperman, S. Shore, J. Rutten, J. Vaughan

View Abstracts
Conference Homepage

On C_\alpha-Compact Subsets
by
Salvador Garcia-Ferreira
Univ. Nacional Autonoma de Mexico
Coauthors: M. Sanchis, A. Tamariz-Mascarua

We say that a subset B of a space X is C_\alpha-compact in X if for every continuous function f: X --> R^\alpha we have that f(B) is compact. This is a slight generalization of the \alpha-pseudo-compactness concept introduced by Kennison in 1962. We present several properties of these subsets. In particular, we give an easy proof of the fact that if B_i is a C_\alpha-compact subset of the topological group G_i, for every i in I, then \prod_{i in I} B_i is C_\alpha-compact in \prod_{i in I} G_i. We estimate the degree of psedocompacness of locally compact, pseudocompact, non-compact spaces; of the product pseudocompact spaces when the product is psedocompact. The degree of pseudocompactness of a psedocompact space is compared with some other cardinal functions. Several results from the literature are improved; in particular, the main results from the Kennison article. We also list several open questions.

Date received: April 12, 1996