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- Author or Editor: Ákos Császár x
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The fundamental concepts in topological spaces, in particular separation axioms, are presented in a manner that open sets are replaced by more general ones.
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).
We define weak structures and show that these structures can replace in many situations generalized topologies or minimal structures.
Summary In the paper , several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.
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.
The investigations in  are made more precise by considering not only separation axioms for topological spaces but also those connected with Čech closures.