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$g$ -metrizable spaces and the images of semi-metric spaces

Ying Ge, Shou Lin (2007)

Czechoslovak Mathematical Journal

In this paper, we prove that a space $X$ is a $g$ -metrizable space if and only if $X$ is a weak-open, $π$ and $σ$ -image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $π$ and $m s s c$ -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

Generalizations of Lašnev's theorem

Józef Chaber (1983)

Fundamenta Mathematicae

Generalizations of the uniform convergence

M. Przemski (1991)

Matematički Vesnik

Generalized connected functions

Rudolph Hrycay (1970)

Fundamenta Mathematicae

Generalized continuity and separate continuity

Tibor Neubrunn (1977)

Mathematica Slovaca

Generalized tri-quotient maps and Čech-completeness

Themba Dube, Vesko M. Valov (2001)

Commentationes Mathematicae Universitatis Carolinae

For a topological space $X$ let $𝒦 (X)$ be the set of all compact subsets of $X$ . The purpose of this paper is to characterize Lindelöf Čech-complete spaces $X$ by means of the sets $𝒦 (X)$ . Similar characterizations also hold for Lindelöf locally compact $X$ , as well as for countably $K$ -determined spaces $X$ . Our results extend a classical result of J. Christensen.

Geometric and higher order logic in terms of abstract Stone duality.

Taylor, Paul (2000)

Theory and Applications of Categories [electronic only]