# 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:

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