On the extensibility of closed filters in T$_1$ spaces and the existence of well orderable filter bases
Keremedis, Kyriakos ; Tachtsis, Eleftherios
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 343-353 / Harvested from Czech Digital Mathematics Library
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We show that the statement CCFC = ``{\it the character of a maximal free filter $F$ of closed sets in a $T_1$ space $(X,T)$ is not countable\/}'' is equivalent to the {\it Countable Multiple Choice Axiom\/} CMC and, the axiom of choice AC is equivalent to the statement CFE$_0$ = ``{\it closed filters in a $T_0$ space $(X,T)$ extend to maximal closed filters\/}''. We also show that AC is equivalent to each of the assertions: \newline ``{\it every closed filter $\Cal {F}$ in a $T_1$ space $(X,T)$ extends to a maximal closed filter with a well orderable filter base\/}'', \newline ``{\it for every set $A\neq \emptyset $, every filter $\Cal {F} \subseteq \Cal {P}(A)$ extends to an ultrafilter with a well orderable filter base\/}'' and \newline ``{\it every open filter $\Cal {F}$ in a $T_1$ space $(X,T)$ extends to a maximal open filter with a well orderable filter base\/}''.

Publié le : 1999-01-01
Classification:  03E25,  54A20,  54A35,  54D10 
@article{119091,
     author = {Kyriakos Keremedis and Eleftherios Tachtsis},
     title = {On the extensibility of closed filters in T$\_1$ spaces and the existence of well orderable filter bases},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {343-353},
     zbl = {0977.03025},
     mrnumber = {1732656},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119091}
}

Keremedis, Kyriakos; Tachtsis, Eleftherios. On the extensibility of closed filters in T$_1$ spaces and the existence of well orderable filter bases. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 343-353. http://gdmltest.u-ga.fr/item/119091/

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