Some Relative Supra-separation Axioms On Supra-topological Spaces

Some definitions of relative supra-separation axioms and relative strongly supra-separation axioms in supra topological spaces are given.The ralationship between relative supra-separation axioms and supra hereditary of relative supra-separation axioms are studied.We prove the established relationship,and for the unestablished relationship,we construct with corresponding examples to illustrate.The content of this article is divided into five chapters.In the first chapter,we mainly introduce the research background,foreign outside research status of the literature review,research significance and innovation.In the second chapter,we mainly introduce some basic definitions that ralate to the research results of this paper.In the third and fourth chapters,a variety of located methods that non-empty subspace Y of X are investigated,the relationship between several super-T(i=1,2,3,4)and supra hereditary are investigated.In the last chapter,the main research results of this paper are summarized.The main results are as follows:1.If a subspace Y of X is(strongly)S*-T2in X,then Y is(strongly)S*-T1 in X.2.If a subspace Y of X is S*-Ti(i=3,4)in X and Y is strongly S*-T1 in X,then S*-Ti-1(i=3,4)in X.3.If a subspace Y of X is1-S-Ti(i=3,4)in X,then Y is S*-Ti(i=3,4)in X.4.If a subspace Y of is 1-S-T4 in X and Y is strongly in X,then Y is l-S-T3 in X5.If a subspace Y of X is strongly S*-T3 in X and X is S*-T1,then Y is strongly S*-T2 in X.6.If a subspace Y is strongly S*-T4 in X and Y is strongly S*-T1 in X,then Y is strongly S*-T3 in X.7.Let W be non-empty set and W(?)Y(?)Z(?)X(i)If Y is(strongly)S*-Ti(i=1,2,3)in X,then W is(strongly)S*-Ti(i=1,2,3)in Z.(ii)If Y is j-S-T3(j=1,2),then W is j-S-T3(j=1,2)in Z.8.A property of being relative(strongly)S*-T4 and relative j-S-T4(j=1,2)is not supra hereditary.