A topological space is connected if and only if the only sets that are both open and closed in the space are the entire space itself and the emptyset
From Maths
Contents
Statement
Let [ilmath](X,\mathcal{ J })[/ilmath] be a topological space, then[1][2]:
- [ilmath](X,\mathcal{ J })[/ilmath] is connected if and only if the only two sets that are both open and closed in [ilmath](X,\mathcal{ J })[/ilmath] are [ilmath]X[/ilmath] itself and [ilmath]\emptyset[/ilmath]
Proof
Grade: C
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The message provided is:
See Connected_(topology)#Equivalent_definition if stuck, but it's pretty easy
This proof has been marked as an page requiring an easy proof
References