The aim of this paper is to introduce and study the notions of  (resp., pre, semi, )-open sets in terms of an ideal I. These concepts generalize the usual notions of  (resp., pre, semi, ) open sets. Also, several of their topological properties are investigated.

In this paper, we introduce intuitionistic fuzzy semi pre open (closed) sets and intuitionistic fuzzy semi pre continuous mappings in intuitionistic fuzzy topological spaces in Sostak’s sense. Also we investigate the characteristic properties of these sets and mappings.

The concept of fuzzy set was introduced by Zadeh in his classical paper [1]. This concept provides a natural foundation for treating mathematically the fuzzy phenomena, which exist pervasively in our real world, and for building new branches of fuzzy mathematics. In the area of Fuzzy Topology, introduced by Chang [2], much attention has been paid to generalize the basic concepts of General Topo...

Shabir and Naz in [25] introduced the notion of soft topological spaces. They defined basic notions of soft topological spaces such as open soft sets, closed soft sets, soft subspaces, soft closure, soft nbd of a soft point, soft separation axioms, soft regular spaces, soft normal spaces and they established their several properties. Min in [19] investigated some properties of such soft separat...

The notion of -open sets in a topological space was studied by Velicko. Usha Parmeshwari et.al. and Indira introduced the concepts b# *b open respectively. Following this Ekici et. al. notions e-open e-closed mixing closure, interior, -interior -closure operators. In paper some new namely e#-open *e-open are defined their relationship with other similar concetps spaces will be investigated.

Soft set theory [1] was firstly introduced byMolodtsov in 1999 as a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. He has shown several applications of this theory in solvingmany practical problems in economics, engineering, social science, medical science, and so forth, in [1]. In the recent years, papers about soft sets theory and their applications ...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

in this study, we investigate the further properties of quasi irresolute topological groupsdened in [20]. we show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at eg, then f is irresolute on g. later we prove that in a semi-connectedquasi irresolute topological group (g; ; ), if v is any symmetric semi-open neighborhood ofeg, then g is generated by v...