[Quotes added]
In article
<26641995.1209783286823.JavaMail.jakarta@[EMAIL PROTECTED]
>, amu
<amu786la@[EMAIL PROTECTED]
> wrote:
>In article <020520082220496207%plsperry@[EMAIL PROTECTED]
>, Paul Sperry
<plsperry@[EMAIL PROTECTED]
> wrote:
>
>> 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.
I meant to write that R is locally path-connected.
> i know this example but don't know how to write the proof
The example says your conjecture is wrong: X and Y are locally
path-connected, A is connected but is not path-connected. [Of course
any path-connected set is connected.]
What is it that you can't prove?
[If you reply (feel free) please be sure to quote this post so people
will know what you are talking about.]
--
Paul Sperry
Columbia, SC (USA)
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