Lecture 1 - Topological Spaces, Continuity, and Homeomorphism

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In this lecture we cover the basics of topological spaces and motivate algebraic topology.

00:00 What is Algebraic topology
06:00 Motivation for Topological Spaces
13:47 Definition of Topological Spaces
26:02 Subspaces
41:48 Continuous functions
46:41 Homeomorphism

Gabriel Islambouli

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This is the best lecture on topology there is, no questions asked. All the questions a beginner can have are answered, the examples are very thorough in ironing out all the quirks. Genius.

chickn

This is the "perfect" introduction not only to Algebraic Topology but also to General Topology!

Thanks Gabriel, you are one of the best !

omeroral

*Corrections* : At 45:41, X should have the trivial topology. - Thanks Ted

gabrielislambouli

I have watched until around minute 9 so far and I would like to thank you very much for this wonderful introduction!

bestmathematician

You are a extremely talented lecturer. Thank you so much for sharing your lectures!

darrenpeck

Wonderful introduction explaining homotopy and homology. Brilliant!

darrenpeck

Great videos professor! Thank you so much

jennyguanniqu

Closed is dual to open -- clopen or De Morgan's laws (duality).
Union is dual to intersection.
Topological holes cannot be shrunk down to zero -- non null homotopic (Janus points).
Points are dual to lines -- the principle of duality in geometry.
"Always two there are" -- Yoda.

hyperduality

can you please provide a link to these lecture notes ? Thanks in advance.

hayderatrah

how can I learn this stuff real fast with low effort?

BigManBand

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