2011•College MathematicsRequires access

Smallest Open Set and Largest Closed Set of a Subset of Topological Space

Kexiu Zhang

Abstract

This paper discusses the smallest open set and largest closed set in a subset of topological space,and show that if X is a T1 space,and A is a subset of X,then there exists the smallest set containing A in the space(the largest closed set contained in A) if and only if A is a open set(closed set).Several examples are giving at the same time to explain the conditions of the theorems.

About this research paper

What this paper is about

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Closed set, Mathematics, Set (abstract data type), Open set, Topological space, Space (punctuation), Connected space, Topology (electrical circuits)