On L-soft merotopies

The goal of this paper is to focus on the notions of merotopy and also merotopology in the soft universe. First of all, we propose L -soft merotopic (nearness) spaces and L -soft guild. Then, we study binary, contigual, regular merotopic spaces and also relations between them. We show that the categ...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2016-12, Vol.20 (12), p.4779-4790
Main Authors: Çetkin, Vildan, Aygün, Halis
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computational Intelligence
Control
Engineering
Foundations
Fuzzy sets
Mathematical Logic and Foundations
Mechatronics
Robotics
Set theory
Topology
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Summary:The goal of this paper is to focus on the notions of merotopy and also merotopology in the soft universe. First of all, we propose L -soft merotopic (nearness) spaces and L -soft guild. Then, we study binary, contigual, regular merotopic spaces and also relations between them. We show that the category of binary L -soft nearness spaces is bireflective in the category of L -soft nearness spaces. Later, we define L -approach soft merotopological (nearness) spaces by giving several examples. Finally, we define a simpler characterization of L -approach soft grill merotopological space called grill-determined L -approach soft merotopological space. We investigate the categorical structures of these notions such as we prove that the category of grill-determined L -approach soft merotopological spaces is a topological category over the category of L -soft topological spaces. At the end, we define a partial order on the family of all L -approach soft grill merotopologies and show that this family is a completely distributive complete lattice with respect to the defined partial order.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-016-2037-x