Let e be a metric space s a subset of e

Reference no: EM13202344

Let E be a metric space, S a subset of E, and let f:E-R be the function which takes the value 1 at each point of S and 0 at each point of the complement of S. Prove that the set of points of E at which f is not continuous is precisely the boundary of S.

Reference no: EM13202344

Questions Cloud

What dimensions will give the largest printed area : A poster has an area of 190 inches squared with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area?

Estimate of the value of the new project : what is your estimate of the value of the new project and what is the IRR of the new project? Should the firm invest in this project or not?

Compute the optimal pricing scheme of the iphone : Suppose that technophiles are willing to pay $400 now for the latest iphone, but only $300 if they have to wait a year. Normal people are willing to pay $250 and their desire to purchase doesn't vary with time.

How fast is the height of the water increasing : An upright cylindrical tank with a radius 5 m is being filled with water at a rate of 4 m cubed/minute. How fast is the height of the water increasing?

Let e be a metric space s a subset of e : Let E be a metric space, S a subset of E, and let f:E-R be the function which takes the value 1 at each point of S and 0 at each point of the complement of S. Prove that the set of points of E at which f is not continuous is precisely the boundary..

What were main benefits from the activities of the goldsmith : By writing more notes than the amount of gold held, the goldsmith could lend the notes and charge interest on them. Did the goldsmith bankers make money out of thin air in a form of legal theft What were the main benefits fromt he activities of the..

How many trees should planted to maximize the yield : An apple orchard has an average yield of 32 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 4 bushels/tree. How many trees should be planted in order to maximize the yield?

How much withdrawals made and the balance left in account : Robertson Inc. wishes to set aside lump sum money to withdraw from and invest in automating parts of its business over the next 5 years. This money is expected to earn compound interest at the rate of 10% per year.

What dimensions will give the largest printed area : A poster is to have an area of 220 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)

User Account

All Pages