A normed space X is said to be strictly convex if for x # y in X with |||| = 1 = ||yl|, we have ||x+y|| < 2. This says that the mid-point (x + y)/2 of two distinct points a and y on the unit sphere of X does not lie on the unit sphere of X, but it lies in the open unit ball U(0, 1) of X. In particular, no line segment lies on the unit sphere. Request explain marked portion

A normed space X is said to be strictly convex if for x # y in X with |||| = 1 = ||yl|, we have ||x+y|| < 2. This says that the mid-point (x + y)/2 of two distinct points a and y on the unit sphere of X does not lie on the unit sphere of X, but it lies in the open unit ball U(0, 1) of X. In particular, no line segment lies on the unit sphere. Request explain marked portion

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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