# INTERIORS AND CLOSURES IN A SET WITH AN OPERATION

• Nakaoka, Fumie ;
• Published : 2014.10.31
• 62 7

#### 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

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#### Acknowledgement

Supported by : JSPS