AlgTop1b: One-dimensional objects (cont.)

[JohnCohorn]

Fascinating lectures, jarring intro music :)



[zwdrff]

Thanks for creating this video. It's much appreciated. 

[Toxie207]

So are both of those knots topologically equivalent to a circle or just the first?

[njwildberger]

Hi Toxie207, As topological spaces, they are both HOMEOMORPHIC to a circle. However as knots, neither are EQUIVALENT to a circle, and they are not equivalent to each other. So we see we must be careful about the meanings of the words homeomorphic and equivalent. In Lecture 2 we will discuss homeomorphism. Later we will discuss knots and equivalence.

[Toxie207]

@njwildberger Thanks. I studied homeomorphisms as part of my work on analysis of Banach Spaces. I imagine there are similarities. It is the concept of equivalence that I guess I'm struggling with.