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  • Author or Editor: Ákos Császár x
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Abstract  

The investigations in [3] are made more precise by considering not only separation axioms for topological spaces but also those connected with Čech closures.

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Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.

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Abstract  

The fundamental concepts in topological spaces, in particular separation axioms, are presented in a manner that open sets are replaced by more general ones.

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Summary  

There is a formula for the interior of a set in a generalized topology composed of the γ-open sets, where γ is a monotonic map in the power set of X. There are known conditions for a γ assuring that this formula is valid. The paper gives essential generalizations for these conditions and contains some applications.

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Summary  

It is proved a rather general version of the statement that if the union of arbitrary elements of a system λ always belongs to λ then the intersections of elements of λ constitute an ultratopology (i.e. a topology where intersections of open sets are open).

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The author examines sets with the property int A ˆ int A, where denotes a map- ping with suitable properties from exp X to exp X in a topological space X. Thespecial case =cl is ofparticular importance.

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Abstract

We define weak structures and show that these structures can replace in many situations generalized topologies or minimal structures.

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