BoxTopology

LetXabeatopologicalspaceforeacha?A.
1.In ? Xa,thesetsoftheform ? Ua,where UaisopeninXa...

Question

BoxTopology

LetXabeatopologicalspaceforeacha?A.
1.In ? Xa,thesetsoftheform ? Ua,where UaisopeninXa foreacha?A,formabase
foratopology.
2.Whatdonhoods f? RRlooklikeintheboxtopology? [see8.4(1)].Comparewith
4F3.
	
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David · Accepted Answer

1. Let B = {
∏
Uα|Uα open inXα}. We have to prove that this collection
makes the basis for the box topology. For this we have to verify the
following:
(a) As in the collection, we have
∏
Xα ∈ B, Hence B covers
∏
Xα.
(b) Let
{xα} ∈ (
∏
Uα) ∩ (
∏
Vα),

Box Topology LetX a beatopologicalspaceforeacha? A . 1.In ? X a , thesetsoftheform ? U a , where U a isopeninX a foreacha? A , formabase foratopology. 2.Whatdonhoods f? R R looklikeintheboxtopology?...

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