On the order hereditary closure preserving sum theorem

Jianhua Gong, Ivan L. Reilly

Research output: Contribution to journalArticlepeer-review

Abstract

The main purpose of this paper is to prove the following two theorems, an order hereditary closure preserving sum theorem and an hereditary theorem: (1) If a topological property P satisfies (∑′) and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ∈ V is elementary and possesses P, then X possesses P. (2) Let a topological property P satisfy (∑′) and (β), and be closed hereditary. Let X be a topological space which possesses P. If every open subset G of X can be written as an order hereditary closure preserving (in G) collection of elementary sets, then every subset of X possesses P.

Original languageEnglish
Pages (from-to)267-272
Number of pages6
JournalApplied General Topology
Volume8
Issue number2
DOIs
Publication statusPublished - 2007

Keywords

  • Elementary set
  • Order hereditary closure preserving
  • Sum theorem

ASJC Scopus subject areas

  • Geometry and Topology

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