Trying to understand terms in a problem

[Mr Davis 97]

Here is the problem: Let $C$ be a convex disc in the plane, and $C_1$ and $C_2$ be two translates of $C$. Prove that $C_1$ and $C_2$ are non-crossing, that is, it isn't possible that both $C_1 - C_2$ and $C_2 - C_1$ are non-connected.

Here is my question: What exactly do the terms "non-crossing" and "non-connected" mean? Are these terms coming from topology?

 

[member 587159]

Crossing is defined in your problem.

Connectedness is indeed a term from topology. A topological space $(X, \mathcal{T})$ is connected if the only clopen (= both closed and open) sets are $\emptyset$ and $X$. Or equivalently, $X$ is not a disjoint union of two (non-trivial) open sets.

 

[Mr Davis 97]

So as someone who has a limited understanding of topology, what would be a hint or a first step for this?

 

[member 587159]

So as someone who has a limited understanding of topology, what would be a hint or a first step for this?

How does your book define disk?

 

[Mr Davis 97]

A convex disc is any compact, convex set with non-empty interior

 

[Mr Davis 97]

How does your book define disk?

Any hints? I feel for someones who knows topology this would be an easy problem

 

[member 587159]

Any hints? I feel for someones who knows topology this would be an easy problem

It isn't an easy problem. I can't find a quick proof for your statement. Maybe ask to the person who assigned you this problem. Good luck.