Theorem 7.32. Let X and Y be topological spaces. The projection maps tx,Ty on X×Y are continuous, surjective, and open.

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Definition. A function f : X → Y is an embedding if and only if ƒ :X → f(X) is a
homeomorphism from X to f(X), where f(X) has the subspace topology from Y.
Definition. The projection maps nx : X x Y → X and y : X x Y → Y are defined
by Tx(x, y)
= x and ty(x, y) = y.
Theorem 7.32. Let X and Y be topological spaces. The projection maps Tx, ty on X×Y
are continuous, surjective, and open.
Transcribed Image Text:Definition. A function f : X → Y is an embedding if and only if ƒ :X → f(X) is a homeomorphism from X to f(X), where f(X) has the subspace topology from Y. Definition. The projection maps nx : X x Y → X and y : X x Y → Y are defined by Tx(x, y) = x and ty(x, y) = y. Theorem 7.32. Let X and Y be topological spaces. The projection maps Tx, ty on X×Y are continuous, surjective, and open.
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