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L-Fuzzy θ-N-Compact Spaces

Yang Jian

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Abstract

The notions of θ-topology and θ-N-Compactness are introduced and researched. Main results: (1) θNcompactness is a semi regular property and on L good extension. (2) θ N compactness ia an invariant of weak homomorphisms. (3) The product space of a full θ N compact space and a N compact space is a θ N compact space. (4) For ever weakly induced space (L X,δ),it is θ Ncompact iff its underlying space (X,[δ]) is θcompact. These results show that θ Ncompactness has some good properties.

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What this paper is about

The notions of θ-topology and θ-N-Compactness are introduced and researched. Main results: (1) θNcompactness is a semi regular property and on L good extension. (2) θ N compactness ia an invariant of weak homomorphisms. (3) The product space of a full θ N compact space and a N compact space is a θ N compact space. (4) For ever weakly induced space (L X,δ),it is θ Ncompact iff its underlying space (X,[δ]) is θcompact. These results show that θ Ncompactness has some good properties.

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Available abstract

The notions of θ-topology and θ-N-Compactness are introduced and researched. Main results: (1) θNcompactness is a semi regular property and on L good extension. (2) θ N compactness ia an invariant of weak homomorphisms. (3) The product space of a full θ N compact space and a N compact space is a θ N compact space. (4) For ever weakly induced space (L X,δ),it is θ Ncompact iff its underlying space (X,[δ]) is θcompact. These results show that θ Ncompactness has some good properties.

Key concepts: Compact space, Mathematics, Locally compact space, Space (punctuation), Homomorphism, Continuous functions on a compact Hausdorff space, Pure mathematics, Extension (predicate logic)

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