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1. A semi-open rectangle in the R² plane is a set of the form (x, y) E R² | a≤x

1. A semi-open rectangle in the R² plane is a set of the form (x, y) E R² | a≤x

Algebra & Trigonometry with Analytic Geometry
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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SOLVE STEP BY STEP IN DIGITAL FORMAT 1. A semi-open rectangle in the R² plane is a set of the form (x, y) = R² | a≤x <b,c <y <d = R}. Let B be the set of all half-open rectangles in R². a. Show that B is a basis of a topology TB of R². Is the topology generated by B equivalent to the usual topology of R²? why? b. Show that the relative topology (i.e. subspace topology) of the TA of the line = {(x,y) Ix +y = 0} is the discrete topology of A c. Show that the relative topology (i.e. the subspace topology) of the TB of the line = {x,y) Ix=y } is not the discrete topology of B
Transcribed Image Text:SOLVE STEP BY STEP IN DIGITAL FORMAT 1. A semi-open rectangle in the R² plane is a set of the form (x, y) = R² | a≤x <b,c <y <d = R}. Let B be the set of all half-open rectangles in R². a. Show that B is a basis of a topology TB of R². Is the topology generated by B equivalent to the usual topology of R²? why? b. Show that the relative topology (i.e. subspace topology) of the TA of the line = {(x,y) Ix +y = 0} is the discrete topology of A c. Show that the relative topology (i.e. the subspace topology) of the TB of the line = {x,y) Ix=y } is not the discrete topology of B
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