Let S Connected subset of R^2 and p R^2 accumulation point. Show that {p} union S is conected. What happends if p isnt a acummulation point?

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- Jun 6th 2008, 01:59 PMkezmanOpen set
Let S Connected subset of R^2 and p R^2 accumulation point. Show that {p} union S is conected. What happends if p isnt a acummulation point?

- Jun 6th 2008, 03:46 PMPlato
Proofs on connected sets depend on the sequence of text material you have.

Look for a theorem about the existence of two disjoint open sets that separate .

Note any open set that contains must contain another point of .

But would that separate ?