The standard proofs of the Baire category theorem for complete metric spaces (for compact Hausdorff spaces) use the Principle of Dependent Choice. Goldblatt [1] showed the Baire Category Theorem for complete metric spaces is equivalent to the Principle of Dependent Choice. ..
A compact space $X$ is called $\pi$-monolithic if for any surjective continuous mapping $f:X\rightar...
Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the ...
Summary. As application of complete metric space, we proved a Baire’s category theorem. Then we defi...
AbstractThe status of the Baire Category Theorem in ZF (i.e., Zermelo–Fraenkel set theory without th...
summary:In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statemen...
The formulation of the Baire category theorem found in most elementary topology texts deals with two...
AbstractA space is Baire if every nonempty open set is of second category. Every T1 space is shown t...
AbstractThe notion of a set's depending on a given coordinate in a product space is briefly develope...
AbstractWe prove a generalization of Baire's category theorem for chains or iterates of continuous f...
AbstractA space is a Baire space if the intersection of countably many dense open sets is dense. We ...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on ...
A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is...
AbstractRecall that a Hausdorff space X is said to be Namioka if for every compact (Hausdorff) space...
The class of pseudo-complete spaces defined by Oxtoby is one of the largest known classes ^ with the...
A compact space $X$ is called $\pi$-monolithic if for any surjective continuous mapping $f:X\rightar...
Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the ...
Summary. As application of complete metric space, we proved a Baire’s category theorem. Then we defi...
AbstractThe status of the Baire Category Theorem in ZF (i.e., Zermelo–Fraenkel set theory without th...
summary:In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statemen...
The formulation of the Baire category theorem found in most elementary topology texts deals with two...
AbstractA space is Baire if every nonempty open set is of second category. Every T1 space is shown t...
AbstractThe notion of a set's depending on a given coordinate in a product space is briefly develope...
AbstractWe prove a generalization of Baire's category theorem for chains or iterates of continuous f...
AbstractA space is a Baire space if the intersection of countably many dense open sets is dense. We ...
summary:We show that it is consistent with ZF that there is a dense-in-itself compact metric space $...
The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on ...
A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is...
AbstractRecall that a Hausdorff space X is said to be Namioka if for every compact (Hausdorff) space...
The class of pseudo-complete spaces defined by Oxtoby is one of the largest known classes ^ with the...
A compact space $X$ is called $\pi$-monolithic if for any surjective continuous mapping $f:X\rightar...
Let (K, d) be a separable Baire metric space or a completely metrizable space. It is shown that the ...
Summary. As application of complete metric space, we proved a Baire’s category theorem. Then we defi...