Topology Questions (studying for test)

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Homework Help Overview

The discussion revolves around a topology problem related to the subspace topology of the real line as a subset of R². The original poster is seeking clarification on the topology that the axis creates within the standard topology of R².

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the nature of the topology on the real line, questioning whether open intervals can be equated to circles in this context. There is also a discussion about the appropriateness of continuing the thread versus starting new ones for each question.

Discussion Status

The discussion is ongoing with participants engaging in light-hearted exchanges while attempting to clarify the concepts involved. Some guidance has been offered regarding the nature of open intervals and their relation to the topology in question, but no consensus has been reached.

Contextual Notes

There is an indication of confusion regarding the terminology used in the problem statement, particularly concerning the interpretation of the axis as a subspace. Additionally, there are concerns about thread management and the potential impact on community engagement.

Damascus Road
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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...)
 
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Greetings Damascus Road! :smile:

(type "\text{ Let }" :wink:)

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)
 
Open intervals on the real line?
 
Yup! :biggrin:
 
But are those open intervals also circles?
 
(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 :(
 
Damascus Road said:
But are those open intervals also circles?

they're one-dimensional circles! :biggrin:

(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! :wink:)
 
Ok thanks, I'll start another one :) :)
 

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