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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 6E

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Let X be a topological space having an open cover U1,..., Un with the
property that all k-fold intersections U;, n. NUi are either empty or
contractible for all k = 1,...,n (this is an example of an acyclic cover).
(a) Show that H;(X)= 0 for i >n – 1.
(b) For each n, construct an example of such a space X having nonzero
Ãn-2(X).

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