scholarly journals The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces

2004 ◽  
Vol 182 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Michael G. Charalambous
Keyword(s):  
Metrizable Spaces ◽  
Eberlein Compactifications

scholarly journals Uniform Eberlein compactifications of metrizable spaces

2012 ◽  
Vol 159 (7) ◽  
pp. 1691-1694 ◽  
Author(s):  
Taras Banakh ◽  
Arkady Leiderman
Keyword(s):  
Metrizable Spaces ◽  
Eberlein Compactifications

scholarly journals On Eberlein compactifications of metrizable spaces

2002 ◽  
Vol 171 (3) ◽  
pp. 223-234 ◽  
Author(s):  
Takashi Kimura ◽  
Kazuhiko Morishita
Keyword(s):  
Metrizable Spaces ◽  
Eberlein Compactifications

Universal elements for families of separable metrizable spaces

1998 ◽  
Vol 91 (6) ◽  
pp. 3387-3415
Author(s):  
D. N. Georgiou ◽  
S. D. Iliadis
Keyword(s):  
Metrizable Spaces

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Optimal metrics on metrizable spaces

1971 ◽  
Vol 22 (1) ◽  
pp. 660-663
Author(s):  
Ludvik Janos
Keyword(s):  
Metrizable Spaces
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