Continuity and constructions

Concepts

• Continuous function between topological spaces 10 exercisesA function f:X→ Y between topological spaces (X,T_X) and (Y,T_Y) is continuous if the preimage of every open set V of Y is an ope…
• Homeomorphism 10 exercisesA bijection f between topological spaces X and Y that is continuous and whose inverse f^-1 is also continuous.
• Subspace topology 10 exercisesThe topology T_A on a subset A of a topological space (X,T) whose open sets are the intersections of A with the open sets U of X.
• Product topology 10 exercisesThe topology on the product X× Y of two spaces (X,T_X) and (Y,T_Y) that has as basis B the sets U× V with U and V open.
• Quotient topology 10 exercisesThe topology T_q on Y determined by a surjective function q:X→ Y from a space (X,T), whose open sets are the V⊆ Y with q^-1(V) op…