In a topological space (X,t) a subset Ac X is called: pre open if Ac...

 

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In a topological space (X,t) a subset Ac X is called: pre – open if Ac int(cl(A))) "ACA° " ii) semi – open if Ac c(int(A))) "ACA-". iii) a- open if Acint(cl(int(A))) "ACA iv) B-open if Accl(int(cl(A))) "ACA°-". i) -O 11 Show that: a) the family of pre-open sets is closed under arbitrary union. b) the family of a-open sets equals the intersection of the families of pre- open and semi – open sets. | | c) the family of B-open sets equals the union of the families of pre - open and semi – open sets. In a topological space (X,t) a subset Ac X is called: pre – open if Ac int(cl(A))) "ACA° " ii) semi – open if Ac c(int(A))) "ACA-". iii) a- open if Acint(cl(int(A))) "ACA iv) B-open if Accl(int(cl(A))) "ACA°-". i) -O 11 Show that: a) the family of pre-open sets is closed under arbitrary union. b) the family of a-open sets equals the intersection of the families of pre- open and semi – open sets. | | c) the family of B-open sets equals the union of the families of pre - open and semi – open sets.

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