In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. A topological vector space (TVS) is called a Mackey space if its topology is the same as the Mackey topology. The Mackey topology is the opposite of the weak topology, which is the coarsest topology on a topological vector space which preserves the continuity of all linear functions in the continuous dual. The Mackey–Arens theorem states that all possible dual topologies are finer than the weak topology and coarser than the Mackey topology. (Wikipedia).
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods
Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Here is one of the most important curves in mathematics. It is an example of a set that is connected, but not path-connected, and is very prominent in topology and analysis. Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel
From playlist Topology
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - E.Effros
Edward Effros (UC Los Angeles) / 13.09.17 Title: Some remarkable gems and persistent difficulties in quantized functional analysis (QFA) Abstract: QFA was a direct outgrowth of the Heisenberg and von Neumann notions of quantized random variables. Thus, one replaces n-tuples of reals by c
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Algebraic Topology 1.2 : Homotopy Classes and Properties
In this video, I prove homotopy is an equivalence relation, introduce the homotopy classes of different topological spaces. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fematikaqna@gmail
From playlist Topology
What's a straightedge? Geometry Terms and Definitions
An introduction to a very important geometric tool - the straightedge. It's not the same as a ruler! Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel:
From playlist Socratica: The Geometry Glossary Series
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory
Vigleik Angeltveit: The Picard group of Equivariant Stable Homotopy Theory and the Slice Spectral Sequence 30 September 2021 Abstract: Equivariant stable homotopy groups are usually graded on the real representation ring. But it is possible to grade them on the Picard group instead. I wi
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Antonio Díaz Ramos: Mackey functors for fusion systems
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Fusion systems and equivariant algebraic topology"
From playlist HIM Lectures: Junior Trimester Program "Topology"
Homotopy elements in the homotopy group π₂(S²) ≅ ℤ. Roman Gassmann and Tabea Méndez suggested some improvements to my original ideas.
From playlist Algebraic Topology
Mike Hill - Real and Hyperreal Equivariant and Motivic Computations
Foundational work of Hu—Kriz and Dugger showed that for Real spectra, we can often compute as easily as non-equivariantly. The general equivariant slice filtration was developed to show how this philosophy extends from 𝐶2-equivariant homotopy to larger cyclic 2-groups, and this has some fa
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Whole Foods CEO John Mackey on ending poverty, being libertarian, and more (full video) | Big Think
Whole Foods CEO John Mackey on ending poverty, being libertarian, and more Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ----------------------------------------------------------------------------------
From playlist Best Videos | Big Think
Algebraic Topology 1.1 : Homotopy (Animation Included)
In this video, I will introduce homotopy equivalence, some basic examples of homotopy, and the transitivity of homotopy. I use an animation to intuitively explain these concepts. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://
From playlist Topology
Is your company innovating? A Whole Foods case study. | John Mackey | Big Think
Is your company innovating? A Whole Foods case study. Watch the newest video from Big Think: https://bigth.ink/NewVideo Learn skills from the world's top minds at Big Think Edge: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Ind
From playlist Spark your innovation | Big Think
When 20,000 Dimensions is Not Enough
This video describes exciting new developments using transcriptome datasets of over 20,000 dimensions to predict which new Covid-19 variants pose the greatest risk of escaping our current vaccines. Compare that to the 4 dimensions Einstein used to transform our understanding of space/time
From playlist Summer of Math Exposition Youtube Videos
Apple’s Macintosh Classic - Retro Computer Hardware Overview and Review
Macintosh Librarian Episode 1. Maccy and Ms. Fox go over the Macintosh Classic - Apple’s first low cost Macintosh aimed at under $1000. Thanks for watching the first episode of my Macintosh Librarian Video project! I hope this video brings a smile to your face. It was definitely a fun exp
From playlist Early Microcomputers & PCs
Bachir Bekka - On characters of infinite groups
Let G be a countable infinite group. Unless G is virtually abelian, a description of the unitary dual of G (that is, the equivalence classes of irreducible unitary representations of G) is hopeless, as a consequence of theorems of Glimm and Thoma. A sensible substitute for the unitary dual
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Centrality - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms