on the order hereditary closure preserving sum theorem
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ID: 234829
2007
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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 (Σ′) and is closed hereditary, and if V is an order hereditary closure preserving open cover of X and each V ϵ V is elementary and possesses P, then X possesses P.
(2) Let a topological property P satisfy (Σ′) 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.
| Reference Key |
gong2007appliedon
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|---|---|
| Authors | ;Jianhua Gong;Ivan L. Reilly |
| Journal | Health and quality of life outcomes |
| Year | 2007 |
| DOI |
10.4995/agt.2007.1892
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| URL | |
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