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A new type of generalized closed set via \(\gamma \)-open set in a fuzzy bitopological space. (English) Zbl 1480.54008

Levine first initiated the concept of generalized closed sets in a topological space. Cao, Ganster and Reilly further analyzed this notion and found interesting results. In the meanwhile, further research has been carried out on the same concept in fuzzy topological spaces. Balasubramaniam and Sundaram first studied generalized fuzzy closed sets and generalized fuzzy continuity in fuzzy topological spaces. Palaniappan and Rao came up with the notion of regular generalized closed sets in topological spaces and Park and Park extended this work to the fuzzy environment. Introducing a new approach, Bhattacharya defined generalized regular closed sets, which are different from regular generalized closed sets, and explored various characterizations of these sets in an ordinary topological space. Very recently, Bhattacharya and Chakraborty extended this work in fuzzy topological spaces. Bitopological spaces were first introduced by Kelly and till now various constructive works have been going on in this particular field. Also Fukutake introduced generalized closed sets in bitopological spaces. In this article, the authors study a new type of generalized closed sets in fuzzy bitopological spaces.

MSC:

54A40 Fuzzy topology
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