Disasters in metric topology without choice
Tachtsis, Eleftherios
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 165-174 / Harvested from Czech Digital Mathematics Library
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We show that it is consistent with ZF that there is a dense-in-itself compact metric space $(X,d)$ which has the countable chain condition (ccc), but $X$ is neither separable nor second countable. It is also shown that $X$ has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply {\it the disjoint union of metrizable spaces is normal\/}.

Publié le : 2002-01-01
Classification:  03E25,  54A35,  54D20,  54E35,  54E45,  54F05 
@article{119309,
     author = {Eleftherios Tachtsis},
     title = {Disasters in metric topology without choice},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {165-174},
     zbl = {1072.03030},
     mrnumber = {1903316},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119309}
}

Tachtsis, Eleftherios. Disasters in metric topology without choice. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 165-174. http://gdmltest.u-ga.fr/item/119309/

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