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Posted: **Wed May 11, 2022 10:08 pm**

: Problem 7 Let Be Any Norm On R Let Y A B Rbe Continuous And Let C E A B Be Such That C C Y C Sh 1 (29.58 KiB) Viewed 27 times

• Problem 7. Let | || be any norm on R". Let , y: (a, b) + Rbe continuous and let c E (a,b) be such that c(c) + y(c). Show that there exists some 8 >0 so that for all t E (c-8,c + 8) we have r(t) # y(t). (Hint: Use Eo := ||2(C) - yl/2 and the continuity of x and y]