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In the following text, we want to study the behavior of one point compactification operator in the chain Ξ := {Metrizable, Normal, T2, KC, SC, US, T1, TD, TUD, T0, Top} of subcategories of category of topological spaces, Top (where we denote the subcategory of Top, containing all topologicalspaces with property P , simply by P). Actually we want to know, for P∈Ξ and X∈P, the one point compactification of topological space Xbelongs to which elements of Ξ. Finally we find out that the chain {Metrizable, T2, KC, SC, US, T1, TD, TUD, T0, Top} is a forwarding chain with respect to one point compactification operator

chinese journal of mathematics

Study of a Forwarding Chain in the Category of Topological Spaces between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mtext>T</mml:mtext><mml:mtext>0</mml:mtext></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mtext>T</mml:mtext><mml:mtext>2</mml:mtext></mml:msub></mml:mrow></mml:math> with respect to One Point Compactification Operator

Study of a Forwarding Chain in the Category of Topological Spaces between T0 and T2 with respect to One Point Compactification Operator