AlgTop1b: One-dimensional objects (cont.)
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Fascinating lectures, jarring intro music :)
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Thanks for creating this video. It's much appreciated.
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@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.
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113 videosAlgebraic Topology: Short clips- 7:05
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So are both of those knots topologically equivalent to a circle or just the first?
Toxie207 1 year ago
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.
njwildberger 1 year ago