AbstractWe show that two versions of a first countable topological space which are equivalent in ZFC set theory split in the absence of the Axiom of Choice AC. This answers in the negative a related question from Gutierres “What is a first countable space?”
AbstractIn the realm of pseudometric spaces the role of choice principles is investigated. In partic...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
AbstractThe status of the Baire Category Theorem in ZF (i.e., Zermelo–Fraenkel set theory without th...
AbstractWe show that two versions of a first countable topological space which are equivalent in ZFC...
AbstractIn this paper it is studied the role of the axiom of choice in some theorems in which the co...
AbstractVarious topological results are examined in models of Zermelo-Fraenkel set theory that do no...
summary:Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theor...
summary:Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theor...
summary:In set theory without the axiom of choice (${\rm AC}$), we study certain non-constructive pr...
summary:In set theory without the axiom of choice (${\rm AC}$), we study certain non-constructive pr...
Cantor believed that properties holding for finite sets might also hold for infinite sets. One such ...
The definition of first countable space is standard and its meaning is very clear. But is that the c...
Cantor believed that properties holding for finite sets might also hold for infinite sets. One such ...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
Abstract. In set theory without the Axiom of Choice (AC), we observe new relations of the following ...
AbstractIn the realm of pseudometric spaces the role of choice principles is investigated. In partic...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
AbstractThe status of the Baire Category Theorem in ZF (i.e., Zermelo–Fraenkel set theory without th...
AbstractWe show that two versions of a first countable topological space which are equivalent in ZFC...
AbstractIn this paper it is studied the role of the axiom of choice in some theorems in which the co...
AbstractVarious topological results are examined in models of Zermelo-Fraenkel set theory that do no...
summary:Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theor...
summary:Many fundamental mathematical results fail in {\bf{ZF}}, i.e., in Zermelo-Fraenkel set theor...
summary:In set theory without the axiom of choice (${\rm AC}$), we study certain non-constructive pr...
summary:In set theory without the axiom of choice (${\rm AC}$), we study certain non-constructive pr...
Cantor believed that properties holding for finite sets might also hold for infinite sets. One such ...
The definition of first countable space is standard and its meaning is very clear. But is that the c...
Cantor believed that properties holding for finite sets might also hold for infinite sets. One such ...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
Abstract. In set theory without the Axiom of Choice (AC), we observe new relations of the following ...
AbstractIn the realm of pseudometric spaces the role of choice principles is investigated. In partic...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
AbstractThe status of the Baire Category Theorem in ZF (i.e., Zermelo–Fraenkel set theory without th...
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