Question

In: Advanced Math

Let X and Y be T2-space. Prove that X*Y is also T2

Expert Solution

Given and be - spaces .

To prove that is also a - spaces suppose and be two elements of .

and .

As and is a - spaces so there exist two open set and such that , with .

Now since , is open in and , is open in so and is open in .

also as , .

and .

So for all and in there exist two open set and in such that and with .

Hence is also a - spaces .

.

If you have any doubt or need more clarification at any step please comment .

Colby Messinger answered 2 years ago

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