Mathematics Homework Solutions
#19305
Countable and normal
a) Reals with the "usual topology." Is there a way to prove this space is normal other than just saying it is normal because every metric space is normal?
b) Reals with the "K-topology:" basis consists of open intervals (a,b)and sets of form (a,b) - K where K = {1, 1/2, 1/3, ... } Why connected? Why 2nd countable?
This shows how to create statements regarding metric spaces and being connected, second countable, and normal.
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