Fibrewise topological spaces theory be a new branch of mathematics, emerging from algebraic topology. It’s a tool that was essential to homotopy theory. The idea of fibrewise topological spaces is widely used in a wide range of mathematical disciplines, such as groups, differential geometry, and dynamical systems theory. The study of fibrewise topological spaces includes connectivity as one of its key notions. Regarding this, we of the current study construct the concept from fibrewise micro connected topological spaces and explore their main conclusions. Also, the objectives of this article are to define the micro hyperspace, micro ultra-connected and extremally dis connected to investigate its properties. functions that maintain the micro connectivity feature were developed and a characterization of the connected in fibrewise topological space was presented.