Question

Prove that a closed set in the Zariski topology on K1 is either the empty set,...

Prove that a closed set in the Zariski topology on K1 is either the empty set, a finite collection of points, or K1 itself.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Since closed sets are the zero sets of set of polynomials, we obtain closed sets by examining solutions to polynomials.

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
Prove that in R^n with the usual topology, if a set is closed and bounded then...
Prove that in R^n with the usual topology, if a set is closed and bounded then it is compact.
Prove the conjecture or provide a counterexample: Let U ∈ in the usual topology, and let...
Prove the conjecture or provide a counterexample: Let U ∈ in the usual topology, and let F be a finite set. Then (U−F) ∈ in the usual topology.
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T)...
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T) is a T4 - space. Exercise 4.6 The intersection of two half-open intervals of the form [a,b) is either empty or a half-open interval. Thus the family of all unions of half-open intervals together with the empty set is closed under finite intersections, hence forms a topology, which has the half-open intervals as a base.
Prove <=: A x B = empty set <=> A= empty set or B = empty...
Prove <=: A x B = empty set <=> A= empty set or B = empty set?
Let X be a non-empty finite set with |X| = n. Prove that the number of...
Let X be a non-empty finite set with |X| = n. Prove that the number of surjections from X to Y = {1, 2} is (2)^n− 2.
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.
True or False: Any finite set of real numbers is complete. Either prove or provide a...
True or False: Any finite set of real numbers is complete. Either prove or provide a counterexample.
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...
Complex Analysis Proof - Prove: A set is closed if and only if S contains all...
Complex Analysis Proof - Prove: A set is closed if and only if S contains all of its accumulation points.
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the...
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the set A, then the set of equivalence classes of ∼ form a partition of A.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT