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If X and Y are discrete topological spaces, how do I prove X x Y is...

If X and Y are discrete topological spaces, how do I prove X x Y is also discrete?
How would I prove the converse is true, could I ? Very interested. Please explain.

Like to please break down into steps that would make sense. Not sure if I have to use facts of product topology and discrete topology and how to use them.

Math   Advanced-Math   
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