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Connected Spaces : If X is a connected space containing more than one point, and if {x} is closed subset for every x is a member of X show that the number of points in X is infinite.

If X is a connected space containing more than one point, and if {x} is closed subset for every x is a member of X show that the number of points in X is infinite.

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Proof: (By contradiction)
Suppose X contains finite number of points, say X={x_1,x_2,...,x_n}. Since each set with single point {x} is a closed ...

Solution Summary

If X is a connected space containing more than one point, and if {x} is closed subset for every x is a member of X it is shown that the number of points in X is infinite.

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