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Grill Determined L-Approach Merotopological Spaces

100%

Khare M. , Tiwari S.

2010

tom Vol. 99, nr 1

1-12

The present paper is devoted to the study of grill determined L-approachmerotopological spaces. The category having such spaces as objects is shown to be a topological construct (its initial and final structures are provided explicitly). The lattice structure of the family of all these spaces is also discussed. In the classical theory, this category (that is, when L = {0, 1}) is a supercategory of the category of pseudo metric spaces and nonexpansive maps.

L-approach merotopies and their categorical perspective

88%

Khare M. , Tiwari S.

2012

tom Vol. 45, nr 3

699-716

In the present paper, we have made a category theoretic and lattice theoretic study of some nearness-like structures in the L-approach theory. Using L-grills, the notion of L-approach grill structure is introduced as a characterization of L-approach grill merotopy on X; their categorical perspectives and implications are also investigated. A number of illustrative examples are included.