An ideal topological space is a triplet ( , , I), where is a nonempty set, is a topology on , and I is an ideal of subsets of . In this paper, we introduce * -perfect, * -perfect, and * -perfect sets in ideal spaces and study their properties. We obtained a characterization for compatible ideals via * -perfect sets. Also, we obtain a generalized topology via ideals which is finer than using * -perfect sets on a finite set.
Muhammad Shabir and Munazza Naz have shown that every soft topology gives a parametrized family of topologies on a set X. In this paper such a link between topology and soft topology is further discussed.
The aim of this paper is to introduce a single structure which carries the subsets of X as well as the subsets of Y for studying the information about the ordered pair (A, B) of subsets of X and Y. Such a structure is called a binary structure from X to Y. Mathematically a binary structure from X to Y is defined as a set of ordered pairs (A, B) where AX and BY. The purpose of this paper is to introduce a new topology between two sets called a binary topology and investigate its basic properties where a binary topology from X to Y is a binary structure satisfying certain axioms that are analogous to the axioms of topology.
MSC 2010: 54A05, 54A99.
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