≺ X , τ ≻ is a topological space and A ⊆ X , A^− =^? ∩


Question and Answers Forum

All Questions Topic List
Differentiation Questions
Previous in All Question Next in All Question
Previous in Differentiation Next in Differentiation
Question Number 161136 by mnjuly1970 last updated on 12/Dec/21

$≺ X, τ ≻ i s a t o p o l o g i c a l s p a c e$ $a n d A \subseteq X,$ $\bar{A} \overset{?}{=} \underset{F \supset A}{\cap} F (F i s c l o s e d s e t)$
	Answered by mindispower last updated on 12/Dec/21
	$A⊂F ,not empty set A^− ∈{A⊂F,F is closed set} A∈∩_(A⊂F) F⇒A^− ∈closed(∩_(A⊂F) F)=∩_(A⊂F) F F^− =F since F is closed (2) A⊂F ,now lets used that A^− is the smallest closed set that contient A A⊂A^− , ∩_(A⊂F) F=A^− ∩ (∩_(A⊂F−{A^− }) F)⊂A^− ...(2) (1) nd (2)⇒A^− =∩_(A⊂F) F$
	$A \subset F, n o t e m p t y s e t \bar{A} \in {A \subset F, F i s c l o s e d s e t}$ $A \in \underset{A \subset F}{\cap} F \Rightarrow \bar{A} \in c l o s e d (\underset{A \subset F}{\cap} F) = \underset{A \subset F}{\cap} F$ $\bar{F} = F s i n c e F i s c l o s e d$ $(2) A \subset F, n o w l e t s u s e d t h a t \bar{A} i s t h e s m a l l e s t$ $c l o s e d s e t t h a t c o n t i e n t A$ $A \subset \bar{A}, \underset{A \subset F}{\cap} F = \bar{A} \cap (\underset{A \subset F - {\bar{A}}}{\cap} F) \subset \bar{A} . . . (2)$ $(1) n d (2) \Rightarrow \bar{A} = \underset{A \subset F}{\cap} F$
	Commented by mnjuly1970 last updated on 13/Dec/21

	$g r e a t s i r p o w e r b r a v o . . .$
	Answered by mindispower last updated on 12/Dec/21

	$m o r e / q u a t i o n l i k e t h i s s i r p l e a s e$ $m o r p h i s u m m o d u l a r G r o u p s$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum