In article
<12420190.1209774828799.JavaMail.jakarta@[EMAIL PROTECTED]
>, amu
<amu786la@[EMAIL PROTECTED]
> wrote:
> Let X,Y be topological spaces. Consider Z = X x Y and the product
topology
> genearted by the projections p_x, p_y. Let A be a subset of Z.
> Suppose that X,Y are locally path connected. Show that A is connected if
and
> only if A is path connected.
Consider A = { (x, sin(1/x)} : x in R - {0} ) \/ { (0, 0) }.
A is a standard example of a subset of R x R which is connected but not
path-connected. R is, of course, path-connected.
--
Paul Sperry
Columbia, SC (USA)
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