CK (Y,V) is cont. if =1₂5) = cl₂ ( f(s)) 1=1}₁₂ T = subspace top: from R, uval) =discrete top f(x) = { ₁ if x 4-1 if X 21 mt. et, ≤-1 and a pt. ?) case Let S S [1,00). Notice f(s) = {1}. Then clxsx = [1,00)X = [1,00 So cl(s)[, ~] Then f (cl(s)) = {1}. So f (cl 5 ) = {1} = Cly([1]) = clyl- ↑ [17 is closed in (Y, V) D Case Let S (-00,-1]. (HW)
CK (Y,V) is cont. if =1₂5) = cl₂ ( f(s)) 1=1}₁₂ T = subspace top: from R, uval) =discrete top f(x) = { ₁ if x 4-1 if X 21 mt. et, ≤-1 and a pt. ?) case Let S S [1,00). Notice f(s) = {1}. Then clxsx = [1,00)X = [1,00 So cl(s)[, ~] Then f (cl(s)) = {1}. So f (cl 5 ) = {1} = Cly([1]) = clyl- ↑ [17 is closed in (Y, V) D Case Let S (-00,-1]. (HW)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 41E
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