Re: -- boundary of an open set

On Mon, 6 Oct 2008, quasi wrote:
On Mon, 06 Oct 2008 15:23:38 -0400, quasi <quasi@xxxxxxxx> wrote:

If U is a nonempty, non-dense open subset of R^n, with n > 1, must the
boundary of U contain a nontrivial path?

If the answer to my question above is "yes", then perhaps we can try
for more:

If U is a nonempty, non-dense open subset of R^n, with n > 1, must the
boundary of U contain a subset which is homeomorphic to R^(n-1)?

If U is not empty, not dense subset of R,
then bd U has a subset homeomorphic to R^0.

.

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