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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.

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 γ : x F } has the property 𝒫 for each x X . It is shown that every 𝒫 -approximable compact space has 𝒫 , if 𝒫 is one of the following properties: countable tightness, 0 -scatteredness with respect to character, C -closedness, sequentiality (the last holds under MA or 2 0 < 2 1 ). Metrizable-approximable spaces are studied: every compact space in this class has...

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.

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