Totally bounded space

Totally Bounded

In this video, we define total boundedness, which is a beautiful concept from topology, and we show that any compact space must be totally bounded. Enjoy! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel: https://youtube.com/d

From playlist Topology

Every Compact Set in n space is Bounded

Every Compact Set in n space is Bounded 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 Advanced Calculus

Convergent sequences are bounded

Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the

From playlist Sequences

Open and closed sets -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

What are Bounded Sequences? | Real Analysis

What are bounded sequences? We go over the definition of bounded sequence in today's real analysis video lesson. We'll see examples of sequences that are bounded, and some that are bounded above or bounded below, but not both. We say a sequence is bounded if the set of values it takes on

From playlist Real Analysis

Continuous implies Bounded

Continuous implies Bounded In this video, I show that any continuous function from a closed and bounded interval to the real numbers must be bounded. The proof is very neat and involves a straightforward application of the Bolzano-Weierstraß Theorem, enjoy! Bolzano-Weierstraß: https://yo

From playlist Limits and Continuity

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)

Topology: Topological Spaces

This video is about topological spaces and some of their basic properties.

From playlist Basics: Topology

What Is Nothing?

Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?

From playlist Guide to Space

Metric Spaces - Lectures 19 & 20: 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 10th of 11 videos. The course is about the notion of distance. You m

From playlist Oxford Mathematics Student Lectures - Metric Spaces

Metric Spaces - Lectures 21, 22 & 23: 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 11th of 11 videos. The course is about the notion of distance. You m

From playlist Oxford Mathematics Student Lectures - Metric Spaces

Ahlfors Bers 2014 "The complex geometry of Teichmüller space and symmetric domains"

Stergios Antonakoudis (Cambridge University): From a complex analytic perspective, Teichmüller spaces can be realized as contractible bounded domains in complex vector spaces by the Bers embeddings. Bounded Symmetric domains constitute another class of bounded domains that has been extensi

From playlist The Ahlfors-Bers Colloquium 2014 at Yale

Martin Vohralik: A posteriori error estimates and solver adaptivity in numerical simulations

Abstract: We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic s

From playlist Numerical Analysis and Scientific Computing

Mikhail Lyubich: Story of the Feigenbaum point

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi

From playlist Dynamical Systems and Ordinary Differential Equations

Weil-Petersson currents by Georg Schumacher

DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be

From playlist Analytic and Algebraic Geometry-2018

Yuval Peres - 1/3 The cutoff phenomenon and rate of escape for Markov chains

From playlist Spectral properties of large random objects - Summer school 2017

Stephan Mescher (3/10/22): Geodesic complexity of Riemannian manifolds

Geodesic complexity is motivated by Farber’s notion of topological complexity of a space, which gives a topological description of the motion planning problem in robotics. Motivated by this, D. Recio-Mitter recently introduced geodesic complexity as an isometry invariant of geodesic spaces

From playlist Topological Complexity Seminar

Suqi Liu -- Phase transition in noisy high-dimensional random geometric graphs

From playlist Columbia-Princeton Probability Day, May 7, 2021

Math 131 Fall 2018 101018 Continuity and Compactness

Definition: bounded function. Continuous image of compact set is compact. Continuous image in Euclidean space of compact set is bounded. Extreme Value Theorem. Continuous bijection on compact set has continuous inverse. Definition of uniform continuity. Continuous on compact set impl

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)