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The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

We introduce the concepts of gm-continuity, GM-converge to a point on generalized topology and minimal structure spaces. Also, we introduce the notions of gm-T 2 space, gm-closed graph and strongly gm-closed graph on generalized topology and minimal structure spaces. We obtain several characterizations and properties of gm-continuous functions by using the interior operator and closure operator defined on both a generalized topology g and a minimal structure m. Moreover, we investigate some properties for gm-continuous functions by using the notions of gm-T 2 space, gm-closed graph and strongly gm-closed graph.

We investigate various classes of generalized closed fuzzy sets in[0,1]-topological spaces, namely,Wθg-closed fuzzy sets andWδg-closed fuzzy sets. Also, we introduce a new separation axiomFT3/4∗of the[0,1]-topological spaces, and we prove that everyFT3/4∗-space is aFT3/4-space. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy mappings.

The aim of this paper to introduce the concept of almost (µ, µ ) (m,n) -homeomorphism on bigeneralized topological space. Also, we introduce the concept of (µ, µ ) (m,n) -homeomorphism on bigeneralized topological space. Basic properties, characterizations and relationships between (µ, µ ) (m,n) -homeomorphism and almost (µ, µ ) (m,n) -homeomorphism are obtained.