hi

I need to find examples for these two topological spaces:

a. A space such that every sequence has a convergent subsequence, but X is not compact.

b. Space . every infinite set has an accumulation point and is not compact.

thanks

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- Apr 3rd 2011, 02:52 AMaharonidanexample for a non compact space?
hi

I need to find examples for these two topological spaces:

a. A space such that every sequence has a convergent subsequence, but X is not compact.

b. Space . every infinite set has an accumulation point and is not compact.

thanks - Apr 3rd 2011, 08:03 AMroninpro
You probably need to look at topological spaces that are not metrizable. If were a metric space, then condition (a) would actually be equivalent to compactness.

- Apr 3rd 2011, 06:08 PMDrexel28