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 language | English |
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Pages (from-to) | 267-272 |
Number of pages | 6 |
Journal | Applied General Topology |
Volume | 8 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2007 |
Keywords
- Elementary set
- Order hereditary closure preserving
- Sum theorem
ASJC Scopus subject areas
- Geometry and Topology