Abstract

Within this paper, the weaker separation axioms of $T_0$, $T_1$, $R_0$, $T_2$, and $R_1$ are further characterized using mathematical induction, closed sets, convergence, and $T_0$-identification spaces. The results are used to further investigate general topological spaces, to further investigate constant nets and sequences, and finite nets and sequences in topological spaces.

Keywords: $T_0$-space; $T_1$-space; $T_2$-space; $R_0$-space; $R_1$-space.

MSC: 54D10, 54A20

Pages:  61$-$71     

Volume  64 ,  Issue  1 ,  2012