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2011•Unpublished venueRequires access

The compactness relative to a subbase for the topology

Liu De-jin

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Abstract

Covering methods are widely used in rough set theory.The interior and the closure of a subset relative to a subbase for the topology are introduced to study the relationships between the rough sets and the topological space.We introduce the separateness relative to a subbase for the topology on the basis of open set and closed set relative to a subbase,and some properties are also discussed,which generalize separateness in a general topology.

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What this paper is about

Covering methods are widely used in rough set theory.The interior and the closure of a subset relative to a subbase for the topology are introduced to study the relationships between the rough sets and the topological space.We introduce the separateness relative to a subbase for the topology on the basis of open set and closed set relative to a subbase,and some properties are also discussed,which generalize separateness in a general topology.

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Available abstract

Covering methods are widely used in rough set theory.The interior and the closure of a subset relative to a subbase for the topology are introduced to study the relationships between the rough sets and the topological space.We introduce the separateness relative to a subbase for the topology on the basis of open set and closed set relative to a subbase,and some properties are also discussed,which generalize separateness in a general topology.

Key concepts: Subbase, Mathematics, Topology (electrical circuits), Closure (psychology), General topology, Compact space, Set (abstract data type), Topological space

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