Re: subsets of R^2, continuity
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 12 Sep 2006 05:13:04 GMT
In article <1158034277.798177.140980@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Fedor <malabar_carotte@xxxxxxxxx> wrote:
suppose that E, F are two connected subsets of R^2. Is there any
conditions on E,F that ensures that there exists a continuous function
f:E \to R^2 such that f(E)=F. Of course Card(E) >= Card(F), but it
doesn t seems sufficient.
It's sufficient that Card(E) > 1 and F is compact and locally
connected.
Hint: Hahn-Mazurkiewicz theorem.
Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.
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