How do I show 7.35? Could you explain this in great detail? Thank you! Definition. A function f : X → Y is an embedding if and only if f :X → f(X) is ahomeomorphism from X to f(X), where f(X) has the subspace topology from Y.Definition. The projection maps nx : X× Y → X and ty : X ×Y → Y are definedby Tx(x, y) = x and Ay(x, y) = y.Theorem 7.32. Let X and Y be topological spaces. The projection maps Tx, ty on X×Yare continuous, surjective, and open.In fact, the topology on the product space can be characterized as the coarsesttopology that makes the projection maps continuous.Theorem 7.33. Let X and Y be topological spaces. The product topology on X × Y is thecoarsest topology on X × Y that makes the projection maps Tx,Ty on X × Y continuous.Theorem 7.35. Let X and Y be topological spaces. For every y E Y, the subspace X ×{y}of X × Y is homeomorphic to X.

Name: How do I show 7.35? Could you explain this in great detail? Thank you!
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: How do I show 7.35? Could you explain this in great detail? Thank you! Definition. A function f : X → Y is an embedding if and only if f :X → f(X) is ahomeomorphism from X to f(X), where f(X) has the subspace topology from Y.Definition. The projectio