Fibrewise Slightly Perfect Topological Spaces

The primary objective of this paper is to present a new concept of fibrewise topological spaces over B is said to be fibrewise slightly topological spaces over B. Also, we introduce the concepts of fibrewise slightly perfect topological spaces, filter base, contact point, slightly convergent, slightly directed toward a set, slightly adherent point, slightly rigid, fibrewise slightly weakly closed, H.set, fibrewise almost slightly perfect, slightly*.continuous fibrewise slightly* topological spaces respectively, slightly T-e, locally QHC, In addition, we state and prove several propositions related to these concepts.