THEOREM 15.2 | S IS A SUBBASIS FOR THE PRODUCT TOPOLOGY OF XxY

THEOREM 17.11 | EVERY SIMPLY ORDERED SET IS A HAUSDORFF SPACE IN A ORDERED TOPOLOGY

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PROOF OF T EQUALS THE COLLECTION OF UNIONS OF ELEMENTS OF B | TOPOLOGY LEMMA 13.1

THEOREM 17.9 | x IS A LIMIT POINT OF A IFF. EVERY NEIGHBOURHOOD OF x CONTAINS INFINITELY MANY POINTS

LEMMA 13.2 | PROVE THAT C IS A BASIS FOR A TOPOLOGY T ON X.

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A IS CLOSED IN Y if and only if A EQUALS THE INTERSECTION OF CLOSED SETS OF X WITH Y