Interiors and closures in a set with an operation
Commun. Korean Math. Soc. 2014 Vol. 29, No. 4, 555-568
Printed October 1, 2014
Fumie Nakaoka and Nobuyuki Oda
Fukuoka University, Fukuoka University
Abstract : A set with an operation defined on a family of subsets is studied. The operation is used to generalize the topological space itself. The operation defines the operation-open subsets in the set. Relations are studied among two types of the interiors and the closures of subsets. Some properties of maximal operation-open sets are obtained. Semi-open sets and pre-open sets are defined in the sets with operations and some relations among them are proved.
Keywords : operation, interior, closure
MSC numbers : 54A05
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