Show that every subset of a discretespace is both open and closed.
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Proof:
First, let's clarify the definition of a discrete space.
Given a set X, the discrete topology on X is defined by ...
Solution Summary
Open and closed discrete spaces are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
... and closed, so A is open and closed, with cl ... co-countable topology on X is the discrete topology, then ... not connected, there are two disjoint nomempty open sets A ...
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