Re: Topology with locally connected and f(X).
- From: William Elliot <marsh@xxxxxxxxxxxxxxxxxx>
- Date: Mon, 19 Nov 2007 04:13:44 -0800
On Mon, 19 Nov 2007, mina_world wrote:
f : X -> Y is continuous.Counter example.
X is a locally connected space.
Then f(X) is locally connected space.
I think...wrong problem.
f:Z+ -> { 0, 1/n | n in N }
f(n) = 1/n; f(0) = 0
Maybe, I need a condition that f is open map.Counter example. f:R -> Q + {a}, f(R) = {a}
where + is the disjoint sum of Q and {a}.
My thinking is right ?If y = f(x) in open V subset Y, then
x in f^-1(y) subset open f^-1(V)
some open connected U with x in U subset f^-1(V)
and so forth...
.
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