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  • Author or Editor: Ákos Császár x
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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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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

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

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Let a topological s ace X be said to be rarophile i .each rare set is a .nite intersection of semi-o en sets (in the sense that A is semi-o en i .A .cl(int(A))).Various characteri- zations for raro hile spaces,examples of rarophile and non-rarophile spaces,ro erties of raro hile spaces are given and some o en roblems formulated.

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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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