Characterizations of L-convex spaces

Bin Pang; Yi Zhao

Characterizations of L-convex spaces

Bin Pang, Yi Zhao^*

^*Corresponding author for this work

Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

69 Citations (Scopus)

Abstract

In this paper, the concepts of L-concave structures, concave L-interior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave L-interior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the cat-egory of L-convex spaces whenever L is a completely distributive lattice with an order-reversing involution operator.

Original language	English
Pages (from-to)	51-61
Number of pages	11
Journal	Iranian Journal of Fuzzy Systems
Volume	13
Issue number	4
Publication status	Published - 1 Aug 2016
Externally published	Yes

Keywords

Concave L-interior operator
Concave L-neighborhood system
Convex L-closure operator
L-concave structure
L-convex structure

Cite this

Pang, B., & Zhao, Y. (2016). Characterizations of L-convex spaces. Iranian Journal of Fuzzy Systems, 13(4), 51-61.

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AB - In this paper, the concepts of L-concave structures, concave L-interior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave L-interior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the cat-egory of L-convex spaces whenever L is a completely distributive lattice with an order-reversing involution operator.

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Characterizations of L-convex spaces

Abstract

Keywords

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