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Almost g ˜ α -closed functions and separation axioms

O. Ravi, S. Ganesan, R. Latha (2012)

Mathematica Bohemica

We introduce a new class of functions called almost g ˜ α -closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost g ˜ α -closed continuous surjections.

An example for mappings related to confluence

Pavel Pyrih (1999)

Archivum Mathematicum

Confluence of a mapping between topological spaces can be defined by several ways. J.J. Charatonik asked if two definitions of the confluence using the components and quasi-components are equivalent for surjective mappings with compact point inverses. We give the negative answer to this question in Example 2.1.

An example of a space whose all continuous mappings are almost injective

Pablo Mendoza Iturralde (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that all continuous maps of a space X onto second countable spaces are pseudo-open if and only if every discrete family of nonempty G δ -subsets of X is finite. We also prove under CH that there exists a dense subspace X of the real line , such that every continuous map of X is almost injective and X cannot be represented as K Y , where K is compact and Y is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact X , all continuous maps of X onto second...

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