Show that the closure of a connected space is connected.
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A: Thanks for the question :)And your upvote will be really appreciable ;)
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Show that the closure of a connected space is connected.
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- Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.Elaborate on the role of duality in topological spaces.Provide an example of a topological space that is connected but not path-connected,why?