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On $π$ -metrizable spaces, their continuous images and products

Derrick Stover (2009)

Commentationes Mathematicae Universitatis Carolinae

A space $X$ is said to be $π$ -metrizable if it has a $σ$ -discrete $π$ -base. The behavior of $π$ -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly $d$ -separable spaces as those which are the image of a $π$ -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a $π$ -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a $π$ -metrizable topological group must be metrizable receives...

On Σ-products of Σ-spaces

Yukinobu Yajima (1984)

Fundamenta Mathematicae

One more remark on reflections

Miroslav Hušek (1967)

Commentationes Mathematicae Universitatis Carolinae

One-point compactification on convergence spaces.

So, Shing S. (1994)

International Journal of Mathematics and Mathematical Sciences

Openly factorizable spaces and compact extensions of topological semigroups

Taras O. Banakh, Svetlana Dimitrova (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its Stone-Čech compactification $β S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f : S \to Y$ to a second countable space $Y$ can be written as the composition $f = g \circ p$ of an open map $p : X \to Z$ onto a second countable space $Z$ and a map $g : Z \to Y$ . We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.

Orbit spaces of the hyperspace of a graph which are Hilbert cubes

R. E. Heisey, J. E. West (1988)

Colloquium Mathematicae

Ordered spaces and quasi-uniformities on spaces of continuous order-preserving functions.

Koena Rufus Nailana (2000)

Extracta Mathematicae

In this paper we introduce and investigate the notions of point open order topology, compact open order topology, the order topology of quasi-uniform pointwise convergence and the order topology of quasi-uniform convergence on compacta. We consider the functorial correspondence between function spaces in the categories of topological spaces, bitopological spaces and ordered topological spaces. We obtain extensions to the topological ordered case of classical topological results on function spaces....

Ordinal invariants and epimorphisms in some categories of weak Hausdorff spaces

Dikran N. Dikranjan, Eraldo Giuli (1986)

Commentationes Mathematicae Universitatis Carolinae

Ordinal products of topological spaces

Vitalij Chatyrko (1994)

Fundamenta Mathematicae

The notion of the ordinal product of a transfinite sequence of topological spaces which is an extension of the finite product operation is introduced. The dimensions of finite and infinite ordinal products are estimated. In particular, the dimensions of ordinary products of Smirnov's [S] and Henderson's [He1] compacta are calculated.

Displaying 181 – 189 of 189

Currently displaying 181 – 189 of 189