In this video, I discuss the notion of sequential compactness, which is an important concept used in topology and analogy. I also explain the similarities and differences between sequential compactness and covering compactness. Compactness: https://youtu.be/xiWizwjpt8o Bolzano-Weierstrass
From playlist Topology
Compact sets enjoy some mysterious properties, which I'll discuss in this video. More precisely, compact sets are always bounded and closed. The beauty of this result lies in the proof, which is an elegant application of this subtle concept. Enjoy! Compactness Definition: https://youtu.be
From playlist Topology
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
The single, most important concept in topology and analysis: Compactness. This is explained via covers, which I'll define as well. There are tons of applications of this concept, which you can find in the playlist below Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13v
From playlist Topology
Every Closed Subset of a Compact Space is Compact Proof
Every Closed Subset of a Compact Space is Compact Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Algebraic Topology - 5.3 - Mapping Spaces and the Compact Open Topology
Description of the adjunction (X \times -, Top(X,-))
From playlist Algebraic Topology
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology
We define the compact open topology on mapping spaces.
From playlist Algebraic Topology
"It's perfectly normal", σ-compact, continua and equivalence relations Top PhD Qual Probs (Stream 3)
Just practicing some arguments from topology qualifying exam problems. Hanging out here instead of on Twitch. Hangout on Twitch: https://www.twitch.tv/chalknd Tweet Tweet: https://twitter.com/NateDLock _____________________ Last PhD Update: https://youtu.be/Q_uwvbIi5DQ Last CHALK video: h
From playlist CHALK Streams
Stone-Čech Compactification of Discrete Spaces and The Space of Ultrafilters Top PhD Qual (Stream 4)
Went over the construction of the Stone-Čech compactification for discrete spaces by way of the space of ultrafilters to practice some arguments for my topology qualifying exam. I also show that the βD is zero-dimensional for an arbitrary discrete space D. Which is the exact same proof tha
From playlist CHALK Streams
MAST30026 Lecture 12: Function spaces (Part 4)
We completed the proof that the adjunction property holds for the space of continuous functions from a locally compact Hausdorff space, reminded ourselves of some of the immediate consequences of this theorem, and then began motivating the construction of a metric on function spaces. Lect
From playlist MAST30026 Metric and Hilbert spaces
Big fiber theorems and ideal-valued measures in symplectic topology - Yaniv Ganor
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Big fiber theorems and ideal-valued measures in symplectic topology Speaker: Yaniv Ganor Affiliation: Technion Date: October 22, 2021 In various areas of mathematics there exist "big fiber theorems", these a
From playlist Mathematics
MAST30026 Lecture 8: Compactness I
This is the first of several lectures on compactness. I recalled the proof of the Bolzano-Weierstrass theorem, defined sequential compactness in metric spaces and the characterisation of continuity of functions in terms of limits, and proved that the image of a compact set is compact. Lec
From playlist MAST30026 Metric and Hilbert spaces
Every Set with the Cofinite Topology is Compact
In this video I will show you how to prove that every set with the cofinite topology is a compact topological space. If you enjoyed this video please consider sharing, liking, or subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lm
From playlist Topology
Manifolds - Part 8 - Compactness
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From playlist Manifolds
Manifolds - Part 8 - Compactness [dark version]
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From playlist Manifolds [dark version]
In this video, I discuss the finite intersection property, which is a nice generalization of the Cantor Intersection Theorem and a very elegant application of compactness. Enjoy this topology-filled adventure! Compactness: https://youtu.be/xiWizwjpt8o Cantor Intersection Theorem: https:/
From playlist Topology
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology