Difference between revisions of "Connected (topology)"

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Revision as of 14:03, 13 February 2015

Definition

A topological space

$$(X,\mathcal{J})$$ is connected if there is no separation of $$X$$

Separation

This belongs on this page because a separation is only useful in this definition.

A separation of

$$X$$ is a pair of two non-empty open sets $$U,V$$ where $$U\cap V=\emptyset$$ where $$U\cup V=X$$