Author(s): Intesar Harbi and Ahmed Ghanawi Jasim

Abstract: This research aims to introduce and explore a new type of manifold space, paving the way for a more detailed study. We begin by defining a new open set ($\widetilde{\mathrm{<em>bc</em>}}$-open) based on filter convergence. Building on this foundation, we define the $\widetilde{\mathrm{<em>bc</em>}}$-chart and $\widetilde{\mathrm{<em>bc</em>}}$-atlas, assuming that the functions involved are $\widetilde{\mathrm{<em>bc</em>}}$-homeomorphisms. The study is then extended to cover functions that are $\widetilde{\mathrm{<em>bc</em>}}$-diffeomorphisms, following a precise definition of this pseudo $\widetilde{\mathrm{<em>bc</em>}}$-smooth manifold. Additionally, we examine functions between multiple manifolds and introduce the concepts of $\widetilde{\mathrm{<em>bc</em>}}$-covering spaces and $\widetilde{\mathrm{<em>bc</em>}}$-covering maps. Finally, we discuss various ideas related to the topic.

DOI: 10.22271/maths.2025.v10.i2a.1979

Pages: 46-49 | Views: 217 | Downloads: 13

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