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  • Author or Editor: Á. Császár x
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The author adds some useful remarks to the former paper.

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Abstract  

The purpose of the paper is to show that the construction leading from a topology and an ideal of sets to another topology remains valid, together with a lot of applications, if topology is replaced by generalized topology and ideal by hereditary class.

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Abstract  

The concept of normality is defined for generalized topologies in the sense of [1], a few properties of normal spaces are proved, and their characterization with the help of a suitable form of Urysohn’s lemma is discussed.

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Abstract  

The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is replaced by a generalized topology.

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Abstract  

It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following the paper [3], we discuss some questions related to this construction.

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Abstract  

As generalization of the construction of I-τ where τ is a topology and I is an ideal [11], and similarly of

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
-µ where µ is a generalized topology and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
is a hereditary class [5], we introduce generalized topologies starting from two generalized topologies µ and µ′.

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Abstract  

The definition of the product of topologies is generalized in such a way that topologies are replaced by generalized topologies in the sense of [3].

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Abstract  

It is shown that the theory of δ-and θ-modifications of topological spaces (see [3]) can be generalized for the case when the topology is replaced by a generalized topology in the sense of [1].

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