Abstract: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 … Show more
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