arXiv subjects
Publications and source records attributed to Arun K. Srivastava.
We show that the category $L\textbf{-Top}_{0}$ of $T_{0}$-$L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L\textbf{-Top}$ of $L$-topological spaces and the category $L\textbf{-Sob}$ of sober $L$-topological spaces is the epireflective hull of Sierpinski $L$-topological space in the category $L\textbf{-Top}_{0}$.
We show that the epireflective hull of the Q-Sierpinski space in the category Q-$TOP_0$ of $T_0$ Q-topological spaces is the category Q-SOB of Q-sober topological spaces.
S.A. Solovyov (2008) has recently introduced the notion of a Q-topological space (and Q-continuous maps between them), where Q is a fixed member of a variety of Omega-algebras, which in turn gives rise to the category Q-TOP of such spaces. The purpose of this note is to give a characterization of this category (in a large class of categories), in terms of a 'Sierpinski-like' object, which is similar to the one given by E.G. Manes in 1976 for the category TOP of topological spaces.