Let X and Y be a topological spaces and assume that A CX and B CY. Then the topology on A x B as a subspace of the product X x Y is the same as the product topology on A x B, where A has the subspace topology inherited from X, and B has the subspace topology inherited from Y.
Let X and Y be a topological spaces and assume that A CX and B CY. Then the topology on A x B as a subspace of the product X x Y is the same as the product topology on A x B, where A has the subspace topology inherited from X, and B has the subspace topology inherited from Y.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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![Theorem[4.1.10]
Let X and Y be a topological spaces and assume that A CX and B CY. Then the
topology on A x B as a subspace of the product X x Y is the same as the product
topology on A x B, where A has the subspace topology inherited from X, and B
has the subspace topology inherited from Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F784177b1-a771-4e2d-8a50-2acb13da6e83%2Fadd59982-476a-4353-a76b-01779bdfe7a3%2Fwi8xwxw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem[4.1.10]
Let X and Y be a topological spaces and assume that A CX and B CY. Then the
topology on A x B as a subspace of the product X x Y is the same as the product
topology on A x B, where A has the subspace topology inherited from X, and B
has the subspace topology inherited from Y.
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