Additional characterizations of the $T_2$ and weaker separation axioms

Charles Dorsett

Additional characterizations of the $T_{2}$ and weaker separation axioms

Authors

Charles Dorsett Texas A&M University – Commerce Author

Keywords:

T_{0}

-space,

T_{1}

-space,

T_{2}

-space,

R_{0}

-space,

R_{1}

-space

Subjects:

54D10, 54A20

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.