(adsbygoogle = window.adsbygoogle || []).push({}); Continuous Bijection f:X-->X not a Homeo.

Hi, All:

A standard example of a continuous bijection that is not a homeomorphism is the

map f:[0,1)-->S^1 : x-->(cosx,sinx) ; for one, S^1 is compact, but [0,1) is not,so

they cannot be homeomorphic to each other.

Now, I wonder if it is possible to do this for a continuous bijection of a space to itself,

(with different topologies if necessary) and, if it is possible from a space with itself ,

but a map g: (X,T)-->(X,T) , i.e., with the same topology for domain and codomain.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Continuous Bijection f:X->X not a Homeo.

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**