Characterizations of L-order L-convex spaces

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Su S.H.; Li Q.G.; Liu F.Y.; Li Q.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2022 | Volume:19 | Issue:5 Page(s): 95-109

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Title

Characterizations of L-order L-convex spaces

Author(s)

Su S.H. | Li Q.G" target="_blank"> Li Q.G. | Liu F.Y. | Li Q. | Issue Writer Certificate

Keywords

$L$-order $L$-convexity

$L$-enclosed $L$-order

$L$-order $L$-convex filter

$L$-order $L$-concavity

$L$-order convergence structure

Abstract

In this paper, the concepts of $L$-enclosed $L$-order space, $L$-order $L$-concave space, $L$-internal $L$-order space and $L$-order $L$-convex filter are introduced. The main results are:(1) the categories of $L$-order $L$-convex spaces, $L$-enclosed $L$-order spaces, $L$-order $L$-concave spaces and $L$-internal $L$-order spaces are isomorphic; (2) the category of $L$-order convergence spaces based on $L$-order $L$-convex filters is topological; (3) there is a Galois correspondence between the category of $L$-order convergence spaces and that of $L$-order $L$-convex spaces.

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