If A is an open subset of X and B is an open subset of Y then is an open subset of .
However, any union of such products, even if it isn't such a product, is an open set.
Hi;
let X={1,2,3}. The topology of X is the induced topology from the usual topology on the real line. Consider the product space X * [a,b], where a,b are real numbers. My question is classify all open sets and closed sets of X*[a,b]. what about 1*[a,b], is it open set?
thank you in advance
If A is an open subset of X and B is an open subset of Y then is an open subset of .
However, any union of such products, even if it isn't such a product, is an open set.
Hint: show every subset of X is open. Why? Consider the set:
(k-ε,k+ε)∩X where 0 < ε < 1 and k = 1,2, or 3, which is clearly open under the induced (subset) topology.
Show this means that if S⊆X, and U⊆[a,b], that SxU is open iff U is.