Additional characterizations of the $T_2$ and weaker separation axioms

Abstract

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