Topology Video Series

QuanPenguin

So much to add, I'm gonna draw up a long term plan, it'll probably be around 100 videos before I even touch compactness. Amazing

micromass

Alright, I've watched everything upto directed sets.
Some remarks:
- in video 21 at 51seconds, you say that the cardinality of N is at least the cardinality of B(x). Is this correct? I'm not a native english speaker, but I found that wierd...

Also, I kind of missed a counterexample of a directed set. But then again, it's not really vital...

It would be nice if you would talk about the specialization pre-order sometimes. This is a really handy concept in algebraic geometry, so it would be nice to see a video about it, or just to see it mentioned...

Did you make a long-term planning for the video series? I'm quite interested in that

QuanPenguin

Hello there. Sorry about the lack of updates but I've had the combination of not having a job, being very ill and moving home in the last week. I should be able to pump out videos starting early next week. I also want to make sure I introduce nets perfectly, and make sure that all my definitions of limit/adherence in terms of neighbourhoods are perfectly sound and understandable.

Also yeah, that countability thing does sound a little strange, oh well, I hope most people watching will have some set theory understanding anyway.

CoolPro

These are awesome! Just so you know I'm a first year undergraduate student and I can understand you PERFECTLY! Except for the bits about countability which I've never seen before but I think I get the idea. A countable set is just one that you can write as a sequence right?

quasar987

Very well done. I'm sure many an undergrad is grateful to you for these clear, concise and colorful explanations.

(CoolPro: You're right that a set is called countable if it can be written as a sequence. But when talking about topological spaces, the word countability usually refers to a property of the topology. There various type of countability properties a topological space can have, and these are generally referred to as "the countability axioms". A given topological space may satisfy some of these axioms or none. You can surely find out what these are on wikipedia.)

ThoughtSpace

Hello all, after a few months of personal problems I can finally revive and hopefully complete this series. I have two new videos out with more on the way. Thanks to everybody for their support in the past, I have a new determination to see this through.

I'm still open to suggestions on how best to introduce closure, which will likely be in a couple of videos time.

http://www.youtube.com/user/ThoughtSpaceZero

micromass

Ah nice, I quite missed your videos I really like the videos about nets by the way!

How do you best introduce closure? Hmm, that's not easy. There are three ways to do so:
- the set of all points of closure
- the smallest closed sets containing the original set
- the set of all convergence points of nets

I think the easiest way is the second. But the first way is more often used...

dendub

What happened to these?