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Displaying 1 – 20 of 1974

$𝒯_{0}$ - and $𝒯_{1}$ -reflections

Maria Manuel Clementino (1992)

Commentationes Mathematicae Universitatis Carolinae

In an abstract category with suitable notions of subobject, closure and point, we discuss the separation axioms $T_{0}$ and $T_{1}$ . Each of the arising subcategories is reflective. We give an iterative construction of the reflectors and present characteristic examples.

$ℵ_{0}$ -spaces and images of separable metric spaces.

Ge, Ying (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

$ℵ_{1}$ -directed inverse systems of continuous images of arcs.

Lončar, Ivan (2000)

International Journal of Mathematics and Mathematical Sciences

$𝒫$ -approximable compact spaces

Mihail G. Tkachenko (1991)

Commentationes Mathematicae Universitatis Carolinae

For every topological property $𝒫$ , we define the class of $𝒫$ -approximable spaces which consists of spaces X having a countable closed cover $γ$ such that the “section” $X (x, γ) = ⋂ {F \in γ : x \in F}$ has the property $𝒫$ for each $x \in X$ . It is shown that every $𝒫$ -approximable compact space has $𝒫$ , if $𝒫$ is one of the following properties: countable tightness, $ℵ_{0}$ -scatteredness with respect to character, $C$ -closedness, sequentiality (the last holds under MA or $2^{ℵ_{0}} < 2^{ℵ_{1}}$ ). Metrizable-approximable spaces are studied: every compact space in this class has...

$ℰ_{B}$ -dimension function of bitopological spaces

M. Jelić (1987)

Matematički Vesnik

$ℵ$ -Dowker spaces

Mary Ellen Rudin (1978)

Czechoslovak Mathematical Journal

A basic approach to the perfect extensions of spaces

Giorgio Nordo (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S $_{1}$ ], [S $_{2}$ ], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.