Topology Question - Regions

Suppose that G is a region and let . Prove that G\{a} is a region.

So far I have divided the proof up into 2 parts, showing that G\{a} is open and showing that it is connected. I have done the open part, but am stuck on the connectedness.

I have assumed for contradiction that G\{a} is disconnected (generally seems to work for this type of question given the definition of connectedness), but cannot see where to get the contradiction from. Help much appreciated.

Re: Topology Question - Regions

Quote:

Originally Posted by

**Speed1991** Suppose that G is a region and let

. Prove that G\{a} is a region.

How is *region* defined?

For example in *Moore Spaces* regions are points sets.

That is axiom 0.

But in other spaces there are more conditions.

Re: Topology Question - Regions

A region is defined as a non-empty connected subset of

Re: Topology Question - Regions