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X-is-a-topological-space-and-A-X-A-F-A-F-F-is-closed-set-




Question Number 161136 by mnjuly1970 last updated on 12/Dec/21
         ≺ X , τ ≻ is a topological space        and   A ⊆ X ,         A^− =^? ∩_(F⊃A) F     ( F is closed set )
X,τisatopologicalspaceandAX,A=?FAF(Fisclosedset)
Answered by mindispower last updated on 12/Dec/21
A⊂F ,not empty set A^− ∈{A⊂F,F is closed set}  A∈∩_(A⊂F) F⇒A^− ∈closed(∩_(A⊂F) F)=∩_(A⊂F) F  F^− =F   since F is closed  (2) A⊂F  ,now lets used that A^−  is the smallest  closed set that contient A  A⊂A^− ,  ∩_(A⊂F) F=A^− ∩  (∩_(A⊂F−{A^− }) F)⊂A^− ...(2)  (1) nd (2)⇒A^− =∩_(A⊂F) F
AF,notemptysetA{AF,Fisclosedset}AAFFAclosed(AFF)=AFFF=FsinceFisclosed(2)AF,nowletsusedthatAisthesmallestclosedsetthatcontientAAA,AFF=A(AF{A}F)A(2)(1)nd(2)A=AFF
Commented by mnjuly1970 last updated on 13/Dec/21
   great sir power  bravo...
greatsirpowerbravo
Answered by mindispower last updated on 12/Dec/21
more/quation like this sir please  morphisum modular Groups
more/quationlikethissirpleasemorphisummodularGroups

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