Question

Real Topology: let A={1/n : n is natural} be a subset of the real numbers. Is...

Real Topology: let A={1/n : n is natural} be a subset of the real numbers. Is A open closed, or neither? Justify your answer.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let the set N of natural numbers be endowed with the cofinite topology (in which a...
Let the set N of natural numbers be endowed with the cofinite topology (in which a set is open if and only if it is empty or its complement is finite). (a) Is N connected? Justify your answer. (b) Is N compact? Justify your answer. (c) Explain why the function f : N → N, n→ n ^3 is continuous. (d) Exhibit a function g : N → N which is not continuous.
For n in natural number, let A_n be the subset of all those real numbers that...
For n in natural number, let A_n be the subset of all those real numbers that are roots of some polynomial of degree n with rational coefficients. Prove: for every n in natural number, A_n is countable.
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find...
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find the infimum and the supremum of S, and prove that these are indeed the infimum and supremum. 2. find all the boundary points of the set S. Prove that each of these numbers is a boundary point. 3. Is the set S closed? Compact? give reasons. 4. Complete the sentence: Any nonempty compact set has a....
Consider two copies of the real numbers: one with the usual topology and one with the...
Consider two copies of the real numbers: one with the usual topology and one with the left-hand-side topology. Endow the plane with the product topology determined by these two topologies. Describe and give three examples of the open sets of the topological subspace { (x,y)| y=x}.
Let n be a positive integer and let U be a finite subset of Mn×n(C) which...
Let n be a positive integer and let U be a finite subset of Mn×n(C) which is closed under multiplication of matrices. Show that there exists a matrix A in U satisfying tr(A) ∈ {1,...,n}
Let S(n) be the statement: The sum of the first n natural numbers is 1/2 n2...
Let S(n) be the statement: The sum of the first n natural numbers is 1/2 n2 + 1/2 n + 1000. Show that if S(k) is true, so is S(k+1).
1.The one-to-one correspondence between the positive rational numbers and the natural numbers implies what conclusion about...
1.The one-to-one correspondence between the positive rational numbers and the natural numbers implies what conclusion about the cardinality of the two sets? 2. Is it possible to form a one-to-one correspondence between the natural numbers and the real numbers? Is either set a proper subset of the other? What is the significance of the answer to these questions?
Using field axioms and order axioms prove the following theorems (i) The sets R (real numbers),...
Using field axioms and order axioms prove the following theorems (i) The sets R (real numbers), P (positive numbers) and [1, infinity) are all inductive (ii) N (set of natural numbers) is inductive. In particular, 1 is a natural number (iii) If n is a natural number, then n >= 1 (iv) (The induction principle). If M is a subset of N (set of natural numbers) then M = N The following definitions are given: A subset S of R...
Let U=​{1,2, 3,​ ...,3200​}. Let S be the subset of the numbers in U that are...
Let U=​{1,2, 3,​ ...,3200​}. Let S be the subset of the numbers in U that are multiples of 4​, and let T be the subset of U that are multiples of 9. Since 3200 divided by 4 equals it follows that n(S)=n({4*1,4*2,...,4*800})=800 ​(a) Find​ n(T) using a method similar to the one that showed that n(S)=800 ​(b) Find n(S∩T). ​(c) Label the number of elements in each region of a​ two-loop Venn diagram with the universe U and subsets S...
Let n be a positive integer and let S be a subset of n+1 elements of...
Let n be a positive integer and let S be a subset of n+1 elements of the set {1,2,3,...,2n}.Show that (a) There exist two elements of S that are relatively prime, and (b) There exist two elements of S, one of which divides the other.