Additional characterizations of the $T_2$ and weaker separation axioms

Charles Dorsett

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.