Please help with exercise 18. LSolve in detail so you can understand the exercise 18.L. Define what is meant bylim sup f = L,lim inf fo.18.M. Show that if f is an upper semi-continuous function on a compact subsetK of RP with values in R, then f is bounded above and attains its supremum on K.18.N. Show that an upper semi-continuous function on a compact set maynot be bounded below and may not attain its infimum.18.0. Show that if A is an open subset of Rº and if f is defined on R to R byf(x) = 1,x E A,0,x ¢ A,then f is a lower semi-continuous function. If A is a closed subset of RP, showthat f is upper semi-continuous.18.P. Give an example of an upper semi-continuous function which has aninfinite number of points of discontinuity.18.Q. Is it true that function on R? to R is continuous at a point if and onlyif it is both upper and lower semi-continuous at this point?

Name: Please help with exercise 18. LSolve in detail so you can understand t
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Please help with exercise 18. LSolve in detail so you can understand the exercise 18.L. Define what is meant bylim sup f = L,lim inf fo.18.M. Show that if f is an upper semi-continuous function on a compact subsetK of RP with values in R, then f is b