User:रायसुंदिर/TopologyDefinitions


 * Zorn's lemma in the partially-ordered set P, every chain has an upper bound $$\Longrightarrow$$ P contains at least one maximal element
 * Open/Closed Map f:X -> Y is an open/closed map if (U open/closed in X $$\Longrightarrow$$ f(U) open/closed in Y)
 * Quotient Map (p:X -> Y is onto) and (V is open in Y $$\Longleftrightarrow$$ p-1(V) is open in X)
 * Quotient Topology (p:X -> Y is quotient map) and (make V open in Y only if p-1(V) is open in X's topology)
 * Retraction if A⊂X, then it's the continuous map r:X -> A where r(a) = a for all a∈A