Answering a question of M. Sakai and partially answering a question of NI. Scheepers, we use the Continuum Hypothesis (CH) to show that, for a slight modification of a space constructed by Dowker in 1955, clopen point-cofinite covers can be diagonalized but there is a sequence of open point-cofinite covers that cannot be diagonalized. Also this space distinguishes between Arhangelskii's alpha(2)-property for C-p(X) and alpha(2)-Property for C-p(X, 2). 2013 Elsevier B.V. All rights reserved.
Dowker-type example and Arhangelskii's alpha(2)-property
BONANZINGA, Maddalena;
2013-01-01
Abstract
Answering a question of M. Sakai and partially answering a question of NI. Scheepers, we use the Continuum Hypothesis (CH) to show that, for a slight modification of a space constructed by Dowker in 1955, clopen point-cofinite covers can be diagonalized but there is a sequence of open point-cofinite covers that cannot be diagonalized. Also this space distinguishes between Arhangelskii's alpha(2)-property for C-p(X) and alpha(2)-Property for C-p(X, 2). 2013 Elsevier B.V. All rights reserved.File in questo prodotto:
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