Proposition Let (X, TX), (Y, Ty) be top. spaces Let be a bijective wap then the following statements are (1) f is homeomorphism (2) => (1) (3) f and f(¹) (2) ⇒ (3) is continuous and closed are continuous. equivalent: (3)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 7E
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Propesition
Let f, X-> Y
het (X, Tx), (Y, Ty) be top. spaces
bijective wmap then the fallowing startoments are equivalent:
be
() t is homromorphism
(2) f is continuous and close
(3) f and priD
(1) (2)
(2) →い
(1)(2)
are continuous.
(2)3(3)
(3) ) (2)
(2)<3)
Transcribed Image Text:Propesition Let f, X-> Y het (X, Tx), (Y, Ty) be top. spaces bijective wmap then the fallowing startoments are equivalent: be () t is homromorphism (2) f is continuous and close (3) f and priD (1) (2) (2) →い (1)(2) are continuous. (2)3(3) (3) ) (2) (2)<3)
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