On $T_1$-reflection of topological spaces

Abstract

This paper deals with some universal spaces. For every topological space $X$, the universal $T_1$ space is viewed as the bottom element of the lattice $\mathcal{L}_X$.
 The class of morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all $T_1$ spaces is characterized. Also, we introduce some new separation axioms and characterize them. Moreover, we characterize topological spaces $X$ for which the universal $T_1$ space associated with $X$ is a spectral space. Finally, we give some characterizations of topological spaces such that their $T_1$-reflection are compact spaces.

Neutrosophic Semi <i>β^F</i>-Contra Continuity in a Neutrosophic Topological Space

“…Lazaar et al [17] studied the T 0 -seperation axioms for a neutro TS. Further, the categorical study of these spaces in the special case of the neutro TS called neutro saturated TSs are discussed.…”