# Open set

• June 6th 2008, 01:59 PM
kezman
Open set
Let S Connected subset of R^2 and p $\in$ R^2 accumulation point. Show that {p} union S is conected. What happends if p isnt a acummulation point?
• June 6th 2008, 03:46 PM
Plato
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 $\{ p \}\cup S$.
Note any open set that contains $p$ must contain another point of $S$.
But would that separate $S$?