Question

If X is a topological space, and A ⊆ X, define the subspace topology on A...

If X is a topological space, and A ⊆ X, define the subspace topology on A inherited from X.

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
Topology Give an example of a topological space that is regular, but not normal. Carefully define...
Topology Give an example of a topological space that is regular, but not normal. Carefully define the terms involved and justify your answers.
TOPOLOGY Prove that a subspace of a first countable space is first countable and that countable...
TOPOLOGY Prove that a subspace of a first countable space is first countable and that countable product (product topology) of first countable spaces is first countable.
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...
Consider the product topology on the plane determined by the left-hand-side topology. Describe and give three...
Consider the product topology on the plane determined by the left-hand-side topology. Describe and give three examples of the open sets of the topological subspace { (x,y)| y=x}.
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}.
Prove that, as a subspace of R with its usual topology, Z has the discrete topology.
Prove that, as a subspace of R with its usual topology, Z has the discrete topology.
Give an example of a topological space X that is Hausdorff, but not regular. Prove that...
Give an example of a topological space X that is Hausdorff, but not regular. Prove that the space X you chose is Hausdorff. Prove that the space X you chose is not regular.
Let f be a continuous from a topological space X to the reals. Let a be...
Let f be a continuous from a topological space X to the reals. Let a be in the reals and let A = {x in X : f(x)=a} Show that A is closed inX.
Prove that if a topological space X has the fixed point property, then X is connected
Prove that if a topological space X has the fixed point property, then X is connected
Let X be a topological space and A a subset of X. Show that there exists...
Let X be a topological space and A a subset of X. Show that there exists in X a neighbourhood Ox of each point x ∈ A such that A∩Ox is closed in Ox, if and only if A is an intersection of a closed set with an open set.