Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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INTERIORS AND CLOSURES IN A SET WITH AN OPERATION

  • Nakaoka, Fumie (Department of Applied Mathematics Faculty of Science Fukuoka University) ;
  • Oda, Nobuyuki (Department of Applied Mathematics Faculty of Science Fukuoka University)
  • Received : 2014.03.19
  • Published : 2014.10.31
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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.

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Acknowledgement

Supported by : JSPS

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