Question

Prove that if T is a discrete topological space (i.e., every subset of T is open)...

Prove that if T is a discrete topological space (i.e., every subset of T is open) and ∼ is any equivalence relation on T , then the quotient space T / ∼ is also discrete topological space. [Hint: It is a very short and straightforward proof.]
Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

12

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. a) State the definition of a topological space. b) Prove that every metric space is...
1. a) State the definition of a topological space. b) Prove that every metric space is a topological space. c) Is the converse of part (b) true? That is, is every topological space a metric space? Justify your answer.
Let X be a topological space with topology T = P(X). Prove that X is finite...
Let X be a topological space with topology T = P(X). Prove that X is finite if and only if X is compact. (Note: You may assume you proved that if ∣X∣ = n, then ∣P(X)∣ = 2 n in homework 2, problem 2 and simply reference this. Hint: Ô⇒ follows from the fact that if X is finite, T is also finite (why?). Therefore every open cover is already finite. For the reverse direction, consider the contrapositive. Suppose X...
Prove or provide a counterexample Let (X,T) be a topological space, and let A⊆X. Then A...
Prove or provide a counterexample Let (X,T) be a topological space, and let A⊆X. Then A is dense iff Ext(A) =∅.
If X and Y are discrete topological spaces, how do I prove X x Y is...
If X and Y are discrete topological spaces, how do I prove X x Y is also discrete? How would I prove the converse is true, could I ? Very interested. Please explain. Like to please break down into steps that would make sense. Not sure if I have to use facts of product topology and discrete topology and how to use them.
Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V...
Suppose V is a finite dimensional inner product space. Prove that every orthogonal operator on V , i.e. <T(u), T(v)> , ∀u,v ∈ V , is an isomorphism.
4. Prove the Following: a. Prove that if V is a vector space with subspace W...
4. Prove the Following: a. Prove that if V is a vector space with subspace W ⊂ V, and if U ⊂ W is a subspace of the vector space W, then U is also a subspace of V b. Given span of a finite collection of vectors {v1, . . . , vn} ⊂ V as follows: Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in the scalar field}...
Let (X,d) be a complete metric space, and T a d-contraction on X, i.e., T: X...
Let (X,d) be a complete metric space, and T a d-contraction on X, i.e., T: X → X and there exists a q∈ (0,1) such that for all x,y ∈ X, we have d(T(x),T(y)) ≤ q∙d(x,y). Let a ∈ X, and define a sequence (xn)n∈Nin X by x1 := a     and     ∀n ∈ N:     xn+1 := T(xn). Prove, for all n ∈ N, that d(xn,xn+1) ≤ qn-1∙d(x1,x2). (Use the Principle of Mathematical Induction.) Prove that (xn)n∈N is a d-Cauchy sequence in...
I did already posted this question before, I did get the answer but i am not...
I did already posted this question before, I did get the answer but i am not satisfied with the answer i did the code as a solution not the description as my solution, so i am reposting this question again. Please send me the code as my solution not the description In this project, build a simple Unix shell. The shell is the heart of the command-line interface, and thus is central to the Unix/C programming environment. Mastering use of...
2. SECURING THE WORKFORCE Diversity management in X-tech, a Japanese organisation This case is intended to...
2. SECURING THE WORKFORCE Diversity management in X-tech, a Japanese organisation This case is intended to be used as a basis for class discussion rather than as an illustration of the effective or ineffective handling of an administrative situation. The name of the company is disguised. INTRODUCTION In light of demographic concerns, in 2012, the Japanese government initiated an effort to change the work environment in order to secure the workforce of the future. Japan is world renowned for its...
Please read the article and answear about questions. Determining the Value of the Business After you...
Please read the article and answear about questions. Determining the Value of the Business After you have completed a thorough and exacting investigation, you need to analyze all the infor- mation you have gathered. This is the time to consult with your business, financial, and legal advis- ers to arrive at an estimate of the value of the business. Outside advisers are impartial and are more likely to see the bad things about the business than are you. You should...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT