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continuous in each variable separately if for eae

continuous in each variable separately if for eae

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 18.11. Let F : X × Y → Z. We say that F is continuous in each variable separately if for each yo in Y, the map h:X → Z defined by h(x) = F(x × yo) is continuous, and for each xo in X, the map k : Y → Z defined by k(y) = F(ro x y is continuous. Show that if F is continuous, then F is continuous in each variable separately. %3D
Transcribed Image Text:Problem 18.11. Let F : X × Y → Z. We say that F is continuous in each variable separately if for each yo in Y, the map h:X → Z defined by h(x) = F(x × yo) is continuous, and for each xo in X, the map k : Y → Z defined by k(y) = F(ro x y is continuous. Show that if F is continuous, then F is continuous in each variable separately. %3D
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