14. For each x ER let Bx = {(x, y) = R² | y ER}, notice that Bx is a subset of R². Show that B = {Bx | x ER} is a basis of a topology for IR2. What are open sets like? With the topology generated by B, does R2 satisfy the Frechet property? With the topology generated by B, is R² Hausdorff?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 46E
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SOLVE STEP BY STEP IN DIGITAL FORMAT
こヅッッシ
A A * ☆ @ ! ! ?? !! ??! ¿¡ !? W X
X
XX
O
14. For each x ER let Bx = {(x, y) E R² | y E R}, notice that Bx is a subset of R².
Show that B = {Bx | x ER} is a basis of a topology for R2. What are open sets like?
With the topology generated by B, does R² satisfy the Frechet property? With the topology generated by B, is R²
Hausdorff?
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT こヅッッシ A A * ☆ @ ! ! ?? !! ??! ¿¡ !? W X X XX O 14. For each x ER let Bx = {(x, y) E R² | y E R}, notice that Bx is a subset of R². Show that B = {Bx | x ER} is a basis of a topology for R2. What are open sets like? With the topology generated by B, does R² satisfy the Frechet property? With the topology generated by B, is R² Hausdorff?
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