Topology Lecture 11: Subspaces
We motivate and define the subspace topology. Then we show under what circumstances open (closed) sets in the subspace and larger space coincide. Finally, we discuss the characteristic property of the subspace topology and summarize some of its key properties.
00:00 Introduction
00:20 Motivation for Subspace Topology
09:51 Definition: Subspace Topology
11:04 Example: Union of Intervals
14:23 Example: Sequence 1/n
17:04 Prop: Open (closed) sets of containing space are open (closed) in subspace
19:07 Prop: If subspace is open (closed), then its open (closed) subsets are open (closed) in containing space
21:10 Characteristic Property of Subspace Topology
26:46 Extending and restricting continuous maps to subspaces
31:58 Prop: Properties of Subspaces
This lecture follows Lee's "Introduction to topological manifolds", chapter 3.
A playlist with all the videos in this series can be found here:
• Topology
Пікірлер: 11
This is a quite motivating introduction, and it really helped a lot. Thank you! Keep going on your research!
@mariusfurter
2 жыл бұрын
You are very welcome! I'm happy you enjoyed the video.
Awesome lecture
I love you
Hi mate, I didn't get the thing about 'yota-s': is this about sequences of subspace S?
@mariusfurter
Ай бұрын
It should be the inclusion map of S into X, i.e. the function that sends each s in S to itself, viewed as an element of the larger space.
@slenbisoobeliut
Ай бұрын
@@mariusfurter oh, now I see the picture, thanks mate, you help me a lot for a research project because I don't have the module in uni)
Great stuff! Could you do a video for quotient topology? :)
@mariusfurter
3 жыл бұрын
Thanks! Quotient spaces will be the topic three videos from now.
Sir please make video of digital line topology
@mariusfurter
2 жыл бұрын
I only just learned about this topic because you mentioned it. So I don't think I can say more about it than you would find by a quick internet search.