All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
An Example of a Closed Continuous Function that is Not Open
An Example of a Closed Continuous Function that is Not Open 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
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus
Reconsidering `functions' in modern mathematics | Arithmetic and Geometry Math Foundations 43
The general notion of `function' does not work in mathematics, just as the general notions of `number' or `sequence' don't work. This video explains the distinction between `closed' and `open' systems, and suggests that mathematical definitions should respect the open aspect of mathemat
From playlist Math Foundations
Field Theory - Algebraically Closed Fields - Lecture 9
In this video we define what an algebraically closed field and assert without proof that they exist. We also explain why if you can find a single root for any polynomial, then you can find them all.
From playlist Field Theory
Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Javascript Closures Tutorial - What makes Javascript Weird...and Awesome Pt 3
What is a closure? In this Javascript Tutorial, we're going to be learning about closures - our 3rd most misunderstood concept of Javascript. Watch the full playlist: https://www.youtube.com/playlist?list=PLoYCgNOIyGABI011EYc-avPOsk1YsMUe_ Hopefully, we're going to break it down enough t
From playlist Javascript Tutorial For Beginners
Daniel Hoffmann, University of Warsaw
May 14, Daniel Hoffmann, University of Warsaw Fields with derivations and action of finite group
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Model Theory of Fields with Virtually Free Group Action - Ö. Beyarslan - Workshop 3 - CEB T1 2018
Özlem Beyarslan (Boğaziçi University) / 29.03.2018 Model Theory of Fields with Virtually Free Group Action This is joint work with Piotr Kowalski. A G-field is a field, together with an acion of a group G by field automorphisms. If an axiomatization for the class of existentially closed
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Sebastian Eterović, UC Berkeley
April 12, Sebastian Eterović, UC Berkeley Existential Closedness and Differential Algebra
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Foundations S2 - Seminar 3 - Skolemisation
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. This season the focus is on the proof of the Ax-Grothendieck theorem: an injective polynomial function from affine space (over the complex numbers) to itself is surjective. This week Will started into t
From playlist Foundations seminar
Foundations S2 - Seminar 4 - Lower Lowenheim-Skolem
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this lecture Will proves the lower Lowenheim-Skolem theorem. The webpage for this seminar is https://metauni.org/foundations/ You can join this seminar from anywhere, on any device, at https://www.
From playlist Foundations seminar
Multi-valued algebraically closed fields are NTP₂ - W. Johnson - Workshop 2 - CEB T1 2018
Will Johnson (Niantic) / 05.03.2018 Multi-valued algebraically closed fields are NTP₂. Consider the expansion of an algebraically closed field K by 𝑛 arbitrary valuation rings (encoded as unary predicates). We show that the resulting structure does not have the second tree property, and
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Field Theory - Algebraically Closed Fields (part 2) - Lecture 10
In this video we should that algebraically closed fields exist and are unique. We assume that the direct limit construction works. The construction here depends on the axiom of choice.
From playlist Field Theory
Commutative Algebra - Integral Closures - part 03 - Integral Closedness is Local (an Normality)
In this video we show that being integrally closed is a local property.
From playlist Integral Closures
Abraham Robinson’s legacy in model theory and (...) - L. Van den Dries - Workshop 3 - CEB T1 2018
Lou Van den Dries (University of Illinois, Urbana) / 27.03.2018 Abraham Robinson’s legacy in model theory and its applications ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHe
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Alexandra SHLAPENTOKH - Defining Valuation Rings and Other Definability Problems in Number Theory
We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
Barbara Koenig: Fixpoint games
HYBRID EVENT Recorded during the meeting "19th International Conference on Relational and Algebraic Methods in Computer Science" the November 5, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other t
From playlist Logic and Foundations
A Set is Closed iff it Contains Limit Points | Real Analysis
We prove the equivalence of two definitions of closed sets. We may say a set is closed if it is the complement of some open set, or a set is closed if it contains its limit points. These definitions are equivalent, so we'll prove a set is closed if and only if it contains its limit points.
From playlist Real Analysis