Thread: discrete topological space

Hello friends,

i need some help with this problem. Any help is welcome

here is the question

Show that a topological space X is discrete if and only if all
subset of X is open

thank you

Originally Posted by donsmith

Show that a topological space X is discrete if and only if all subset of X is open

What is meant by "a topological space X is discrete "?

man my English is horrible , I'm trying to translate the problem

second try,

Show that X is a discrete topological space if and only if every subset of X is open

does the question make any sense?

Originally Posted by donsmith

does the question make any sense?

The reason I asked for a clarification is that some texts do define a discrete topology with open sets being the power set of the underlying set. If that is it, there is nothing to prove.

On the other hand, it may be asking you to prove that the power set of a set is in fact a topology on that set.