‎In this study‎, ‎we investigate topological properties of fuzzy strong‎ b-metric spaces defined in [13]‎. ‎Firstly‎, ‎we prove Baire's theorem for‎ ‎these spaces‎. ‎Then we define the product of two fuzzy strong b-metric spaces‎ ‎defined with same continuous t-norms and show that $X_{1}times X_{2}$ is a‎ ‎complete fuzzy strong b-metric space if and only if $X_{1}$ and $X_{2}$ are‎ ‎complete fu...

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simplyconnected. While functoriality of the topological fundamental group for arbitrary topological spaces remains an open question, the topological fundamental group is always a homogeneous space.

in this article we introduce the concept of $z^circ$-filter on a topological space $x$. we study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $c(x)$,  the ring of real-valued continuous functions on a completely regular hausdorff space $x$. it is observed that $x$ is a compact space if and only if every $z^circ$-filter ...