Sum connectedness in proximity spaces

The notion of sum δ-connected proximity spaces which contain the category of δ-connected and locally δ-connected spaces is defined. Several characterizations of it are substantiated. Weaker forms of sum δ-connectedness are also studied.

operator Proximity in i-Topological Space

another form of -operator defined in this paper by using employing two pillars they are i-topological spaces and the proximity spaces

New Concepts of Dense set in i-Topological space and Proximity Space

A new kind of some topological spaces concepts has been defined in i-topological spaces with respect to proximity spaces in our paper.

On L-fuzzy closure operators and L-fuzzy pre-proximities

The aim of this paper is to investigate the relations among the L-fuzzy pre-proximities, L-fuzzy closure operators and L-fuzzy co-topologies in complete residuated lattices. We show that there is a Galois correspondence between the category of separated L-fuzzy closure spaces and that of separated L-fuzzy pre-proximity spaces and we give their examples.

L-fuzzy pre-proximities, L-fuzzy filters and L-fuzzy grills

This article gives results on fixed complete lattice L-fuzzy pre-proximities, L-fuzzy grills and L-fuzzy filters. Moreover, we investigate the relations among the L-fuzzy pre-proximities , L-fuzzy grills and L-fuzzy filters. We show that there is a Galois correspondence between the category of separated L-fuzzy grill spaces and that of separated L-fuzzy pre-proximity spaces. We introduced the local function associated with L-fuzzy grill and L-fuzzy topology and studied some of its properties. Finally, we build an L-fuzzy topology for the corresponding L-fuzzy grill by using local function.

A note on the category of quasi-proximity spaces

We characterize the separation properties T0 and T1 at a point p in the category of quasi-proximity spaces. Moreover, the (strongly) closed and (strongly) open subobjects of an object, and each of the various notions of connected and compact objects are characterized in this topological category.