A class of spaces containing all generalized absolutely closed (almost compact) spaces

Abstract

The class of θ-compact spaces is introduced which properly contains the class of almost compact (generalized absolutely closed) spaces and is strictly contained in the class of quasicompact spaces. In the realm of almost regular spaces, the class of θ-compact spaces coincides with the class of nearly compact spaces. Moreover, an almost regular θ-compact space is mildly normal (= K-normal). A θ-closed, θ-embedded subset of a θ-compact space is θ-compact and the product of two θ-compact space is θ-compact if one of them is compact. A (strongly) θ-continuous image of a θ-compact space is θ-compact (compact). A space is compact if and only if it is θ-compact and θ-point paracompact.

Keywords

• θ-compact space
• Almost compact (generalized absolutely closed) space
• Nearly compact space
• Quasicompact space
• θ-point paracompact space
• θ-closed (θ-open) set
• θ-limit point
• Almost regular space
• Mildly normal(K-normal) space
• Almost normal space
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