Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
MAST30026 Lecture 2: Examples of spaces (Part 1)
I started with the definition of a metric space, we briefly discussed the example of Euclidean space (proofs next time) and then I started to explain a few natural metrics on the circle. Lecture notes: http://therisingsea.org/notes/mast30026/lecture2.pdf The class webpage: http://therisin
From playlist MAST30026 Metric and Hilbert spaces
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
Weird notions of "distance" || Intro to Metric Spaces
Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Weird, fun
From playlist Cool Math Series
The Limit of a Convergent Sequence in a Metric Space is Unique
The Limit of a Convergent Sequence in a Metric Space is Unique If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com Free Homework Help : https://mathsorcererforums.com/ My FaceBook Page: https://www.facebook
From playlist Metric Spaces
MAST30026 Lecture 13: Metrics on function spaces (Part 2)
I discussed pointwise and uniform convergence of functions, proved that the uniform limit of continuous functions is continuous, and used that to prove that Cts(X,Y) is a complete metric space with respect to the sup metric if X is compact and Y is a complete metric space. Lecture notes:
From playlist MAST30026 Metric and Hilbert spaces
MAST30026 Lecture 18: Banach spaces (Part 2)
I gave a counter-example which shows that the space of functions on an integral pair with the L^p-norm for p finite is not complete, and then I started the process of constructing the completion. We almost got to the end of proving the existence of the completion of a metric space. Lectur
From playlist MAST30026 Metric and Hilbert spaces
Jens Kaad: Exterior products of compact quantum metric spaces
Talk by Jens Kaad in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 24, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
MAST30026 Lecture 18: Banach spaces (Part 3)
I finished (completed!) the construction of the completion of a metric space, and sketched the proof that uniformly continuous functions extend from a metric space to its completion uniquely. I then constructed the completion of a normed space and ended by formally defining L^p spaces. Le
From playlist MAST30026 Metric and Hilbert spaces
Metric Spaces - Lectures 11 & 12: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 6th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Infinite solutions of the singular Yamabe problem in spheres via Teichmüller theory - Paolo Piccione
Variational Methods in Geometry Seminar Topic: Infinite solutions of the singular Yamabe problem in spheres via Teichmüller theory Speaker: Paolo Piccione Affiliation: University of Sao Paulo Date: April 25, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Metric Spaces - Lectures 13 & 14: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 7th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
MAST30026 Lecture 18: Banach spaces (Part 1)
There are many Lipschitz equivalent metrics on Euclidean space, apart from the sup-metric (which we have successfully generalised to function spaces) there are also metrics defined using sums. To generalise those, we need integrals, and the resulting theory leads to Banach spaces. In this
From playlist MAST30026 Metric and Hilbert spaces
MAST30026 Lecture 1: What is space? (Part 1)
I started with three dictionary definitions of "space" and briefly discussed them, before moving on to a survey of the standard abstract notions of space used in mathematics, including metric, topological and Hilbert spaces. In the remainder of the lecture I discussed the connection betwee
From playlist MAST30026 Metric and Hilbert spaces
Yanir Rubinstein - Ricci Flow and the Completion of the Space of Kahler Metrics [2011]
Name: Yanir Rubinstein Event: Workshop on Extremal Kahler Metrics Event URL: view webpage Title: Ricci Flow and the Completion of the Space of Kahler Metrics Date: 2011-03-24 @4:00 PM Location: 102 http://scgp.stonybrook.edu/video_portal/video.php?id=626
From playlist Mathematics