2000
DOI: 10.2307/44154064
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Setwise Quasicontinuity and Π-Related Topologies

Abstract: A function is quasicontinuous if inverse images of open sets are semiopen. We generalize this definition: a collection of functions is setwise quasicontinuous if finite intersections of inverse images of open sets by functions in the collection are semi-open (so a function is quasicontinuous if and only if its singleton is a setwise quasicontinuous set). Two topologies on the same space are Π-related if each nonempty open set (in each) has non-empty interior with respect to the other. This paper demonstrates t… Show more

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“…Two topologies T 1 and T 2 on X are said to be π-related if T 1 πT 2 . Theorem 4.2 [7] (1) π-relation is an equivalence relation on the family of all topologies on X.…”
Section: π-Relationshipmentioning
confidence: 99%
“…Two topologies T 1 and T 2 on X are said to be π-related if T 1 πT 2 . Theorem 4.2 [7] (1) π-relation is an equivalence relation on the family of all topologies on X.…”
Section: π-Relationshipmentioning
confidence: 99%