105 / 677100%3 Lot X be the unit circle in R; that is, X ={(r, y) : + y = 1} and has the%3Dsubspace topology.(i) Show that X\{(1,0)} is homeomorphic to the open interval (0,1).(ii) Deduce that X (0, 1) and X (0, 1).(ii) Observing that for every point a EX, the subspace X\{a} is connected, showthat X 0,1).(iv) Deduce that X is not homeomorphic to any interval.

Answered: Image /qna-images/answer/1bf2b95f-179a-47fa-bdff-10436daccbc2.jpg

3 Lot X be the unit circle in R; that is, X = {(r, y) : + y? = 1} and has the subspace topology. (i) Show that X\{(1,0)} is homeomorphic to the open interval (0,1). (ii) Deduce that X (0, 1) and X 0, 1]. (iii) Observing that for every point a EX, the subspace X\{a} is connected, show that X (0,1). (iv) Deduce that X is not homeomorphic to any interval.

3 Lot X be the unit circle in R; that is, X = {(r, y) : + y? = 1} and has the subspace topology. (i) Show that X\{(1,0)} is homeomorphic to the open interval (0,1). (ii) Deduce that X (0, 1) and X 0, 1]. (iii) Observing that for every point a EX, the subspace X\{a} is connected, show that X (0,1). (iv) Deduce that X is not homeomorphic to any interval.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 63E

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