The aim of this paper is to look at fibrewise slightly issuances of the more important separation axioms of ordinary topology namely fibrewise said to be fibrewise slightly T0 spaces, fibrewise slightly T1spaces, fibrewise slightly R0 spaces, fibrewise slightly T2 spaces, fibrewise slightly functionally T2 spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces. In addition, we announce and confirm many proposals related to these concepts.

The aim of the research is to apply fibrewise multi-emisssions of the paramount separation axioms of normally topology namely fibrewise multi-T0. spaces, fibrewise multi-T1 spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal spaces and fibrewise multi-functionally normal spaces. Also we give many score regarding it.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near topological spaces over B. Also, we introduce the concepts of fibrewise near closed and near open topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near compact and fibrewise locally near compact spaces, which are generalizations of well-known concepts near compact and locally near compact topological spaces. Moreover, we study relationships between fibrewise near compact (resp., fibrewise locally near compact) spaces and some fibrewise near separation axioms.

In this thesis, we introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essent

In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.