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I am having some difficulties understanding why a subset under the usual metric topology of the reals is connected.

How can a set X = (0,1] u (1,2) be connected?

The definition I am using is:

A is disconnected if there exists two open sets G and V and the following three properties hold:

(1) A intersect G ≠ ∅

A intersect V ≠ ∅

(2) A is a proper subset of the union of G and V.

(3) the intersection of G and V is the empty set.

Thanks

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# Confusion with Disconnected sets

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