# suppose that C is a connected set in R^p and that x is a cluster point of C. Show that C U {x} is connected.

*label*Mathematics

*timer*Asked: Oct 16th, 2016

*account_balance_wallet*$5

### Question Description

suppose that C is a connected set in R^p and that x is a cluster point of C. Show that C U {x} is connected.

## Tutor Answer

Attached.

Suppose by contradiction that C x is not connected. There exist disjoint open sets G1 , G2 with

G1 G2 = and C x ...

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