Prove the following: Let {X; : i e I} be an indexed family of topo- logical spaces. Suppose that I is the union of two disjoint subsets J and K. Then II X: ieI is homeomorphic to II X; x IIX: ieJ iEK

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 3TFE: Label each of the following statements as either true or false. The least upper bound of a nonempty...
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Prove the following: Let {X; : i e I} be an indexed family of topo-
logical spaces. Suppose that I is the union of two disjoint subsets J
and K. Then
II X:
ieI
is homeomorphic to
II X: x II X:
iEJ
ieK
Transcribed Image Text:Prove the following: Let {X; : i e I} be an indexed family of topo- logical spaces. Suppose that I is the union of two disjoint subsets J and K. Then II X: ieI is homeomorphic to II X: x II X: iEJ ieK
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