In ZF (i.e., Zermelo-Fraenkel set theory without the Axiom of Choice) the following statements are shown to be equivalent: (1) The axiom of dependent choice. (2) Products of compact Hausdorff spaces are Baire. (3) Products of pseudocompact spaces are Baire. (4) Products of countably compact, regular spaces are Baire. (5) Products of regular-closed spaces are Baire. (6) Products of Čech-complete...

We define $\Delta$-Baire spaces. If a paratopological group $G$ is space, then topological group. Locally pseudocompact spaces, Baire $p$-spaces, $\Sigma$-spaces, products of \v{C}ech-complete spaces are

In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

In this paper, the concepts of pairwise fuzzy Baire bitopological spaces are introduced and characterizations of pairwise fuzzy Baire bitopological spaces are studied. Several examples are given to illustrate the concepts introduced in this paper.

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

We discuss the connection of additive set functions to dual function spaces by means of integrals. Isometrical isomorphisms are presented between: a) bounded contents and the dual of uniformly approximable functions, b) charges on Baire algebras and the duals of bounded, continuous functions over A-topological spaces, c) Hewitt measures on Baire σ-algebras and the duals of continuous functions ...

The main result is the following. Let f:X→Y be a continuous mapping of completely Baire space X onto hereditary weakly Preiss-Simon regular Y such that image every open subset resolvable set in Y. Then Baire. classical Hurewicz theorem about closed embedding rational numbers into metrizable spaces generalized to spaces.