Topology Questions (studying for test)

[Damascus Road]

Greetings all,
I have a test upcoming next week and a lot of problems to solve. I asked in a previous thread whether or not I should just continue to adding to the thread and it seems the answer was yes. I appreciate any help! This is a tough subject.

Anyways, the first one I'm working on. I know it's simple but the wording is confusing me...

Let x = {(x,0) \in R^{2} | x \in R the axis in the plane. Describe the topology that inherits a subspace of R^{2} with the standard topology.

So, it's asking what topology the axis creates? Where the axis is the subspace, right?

(edit: I don't know why spaces within the tex seem to be ignored...)

 

[tiny-tim]

Greetings Damascus Road!

(type "\text{ Let }" )

the topology for R² is little open circles …

so the topology for any line in R² is … ? :wink

(btw, I would start a new thread each time)

 

[Damascus Road]

Open intervals on the real line?

 

[tiny-tim]

Yup!

 

[Damascus Road]

But are those open intervals also circles?

 

[Damascus Road]

(btw, I would start a new thread each time)

You don't think so many threads will annoy people? I don't want to make people mad and turn them off from helping :(

 

[tiny-tim]

But are those open intervals also circles?

they're one-dimensional circles!

(and no, you're far more likely to annoy people by dragging a thread out, and making them feel they have to keep replying to new questions that they weren't expecting! )

 

[Damascus Road]

Ok thanks, I'll start another one :) :)