Exercise 1. topology Consider the set of real numbers R equipped with the excluded point то == {U CR | 0 U or U = R}. (i) Is (R, To) a Hausdorff space? Justify your answer. (ii) Identify the limit point(s) of the sequence (1 + 1/12) DEN in (R,ão).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.
 
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Exercise 1.
topology
Consider the set of real numbers R equipped with the excluded point
то
==
{U CR | 0 U or U = R}.
(i) Is (R, To) a Hausdorff space? Justify your answer.
(ii) Identify the limit point(s) of the sequence (1 + 1/12) DEN in (R,ão).
Transcribed Image Text:Exercise 1. topology Consider the set of real numbers R equipped with the excluded point то == {U CR | 0 U or U = R}. (i) Is (R, To) a Hausdorff space? Justify your answer. (ii) Identify the limit point(s) of the sequence (1 + 1/12) DEN in (R,ão).
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