Prove the following: Suppose that {X; : i e I} and {Y; : j € J} are indexed families of topological spaces. Suppose that a : I → J is a bijection and for all i E I, we have X; homeomorphic to [I¡ej Y;. = Ya(i). Then [I;e1 X; is jEJ

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Prove the following: Suppose that {X; : i E I} and {Y; : j € J}
are indexed families of topological spaces. Suppose that a : I → J
is a bijection and for all i E I, we have X; = Ya(1). Then II¡e1 X; is
homeomorphic to II;ej Yj.
j€J 'j•
Transcribed Image Text:Prove the following: Suppose that {X; : i E I} and {Y; : j € J} are indexed families of topological spaces. Suppose that a : I → J is a bijection and for all i E I, we have X; = Ya(1). Then II¡e1 X; is homeomorphic to II;ej Yj. j€J 'j•
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