Topology onneMessaging | Wyzant TutoringO ME341b5d81269c3376a50a604d × +50a604dea9fd0f0?Expires-D1619696031&Signature=s2JaujQ22NGzqiUV4jQLyvgg~GcWi6DvajZEsmp-TGBW..4/ 7100%+(i) True or False: If a path-connected space X is contractible (i.e. the identity mapid : X X, id(x) = x, is homotopic toX is simply connected (i.e. T(X, xo) is trivial). The converse is not necessarily true.constant mapc: X→ X, c(x) ro), then(ii) Assume X is path connected and 71(X, ro) is abelian (i.e. [S] [g] = [g] * [f] for all[f1. Jg] E 71(X, xo)). Show that for any yo E Y and any two paths a1, a2 connectingro to yo the homomorphisms 1, 2 : T1(X, xo) → T1(X, yo) with P1([S]) = [a,'fa1]and d2(f) [a, fa2] are the same homomorphism.(iii) Let p: X → X be a covering map and assume both X and Xa: (0, 1] → X is a loop based at ro E X and assume yo, 2o E p'{xo}, yo # Zo. If theunique lift a : [0, 1]→ X with ã(0) = yo is such that a(1) = žo, then X is not simplyconnected.are path connected. Say->82

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(i) True or False: If a path-connected space X is contractible (i.e. the identity map id : X X, id(x) = x, is homotopic to a constant map c: X X, c(x) = xo), then X is simply connected (i.e. 1(X, xo) is trivial). The converse is not necessarily true.

(i) True or False: If a path-connected space X is contractible (i.e. the identity map id : X X, id(x) = x, is homotopic to a constant map c: X X, c(x) = xo), then X is simply connected (i.e. 1(X, xo) is trivial). The converse is not necessarily true.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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