(a,b) not homeomorphic to [a,b]

[JG89]

Homework Statement

Show that (0,1) is no homeomorphic to [0,1]

Homework Equations

The Attempt at a Solution

I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness. My only question is, the topology on each space isn't specified. Do I assume it's the subspace topology or what?

In general, when given questions like this, with no topology given, do I just infer from the context of the question which topology I should use?

 

[JG89]

Nevermind guys. Looks like I need to pay more attention. My book says to assume the standard topology unless otherwise noted.

 

[Office_Shredder]

I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness.

This is a pretty awesome way of proving they're not homeomorphic to be honest. I think most people would just show that one is compact and the other is not