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I'm not sure how i'm suppose to show that if Y is a subspace of X, and A is a subset of Y, then the topology A inherits as a subspace of Y is the same as the topology it inherits as a subspace of X.

I know that a subspace is... T_{y}= {Y[tex]\cap[/tex]U| U [tex]\in[/tex]T}

meaning that its open sets consist of all intersections of open sets of X with Y.

and that a subset is every element of A is also an element of B.

pretty much right? so how do i express this in terms of subset and subspace?

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# Subspace vs. subset

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