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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.
How is region defined?Quote:
Originally Posted by Speed1991
Suppose that G is a region and let
For example in Moore Spaces regions are points sets.
That is axiom 0.
But in other spaces there are more conditions.
A region is defined as a non-empty connected subset of
IfQuote:
Originally Posted by Speed1991A region is defined as a non-empty connected subset of
is an open set, then
is connected if and only if any two points of
of horizontal and vertical segments lying in
and
.