In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little interest. The specialization order is often considered in applications in computer science, where T0 spaces occur in denotational semantics. The specialization order is also important for identifying suitable topologies on partially ordered sets, as is done in order theory. (Wikipedia).
http://www.tabletclass.com explains the order of operations
From playlist Pre-Algebra
Orders on Sets: Part 1 - Partial Orders
This was recorded as supplemental material for Math 115AH at UCLA in the spring quarter of 2020. In this video, I discuss the concept and definition of a partial order.
From playlist Orders on Sets
Prealgebra 1.7e - Order of Operations with Exponents
Evaluating expressions, taking the order of operations into account, including some tricky cases involving exponents. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 1 (Complete chapter)
Order of Operations - The Basics
This video introduces the order of operations and provides several examples. http://mathispower4u.yolasite.com/
From playlist Properties of Exponents
Prealgebra 2.07c - Order of Operations
Evaluating expressions for given values of the variables, with an emphasis on correct order of operations. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 2 (Complete chapter)
Prealgebra Lecture 2.5 Part 7: Order of Operations with Integers
From playlist Prealgebra Playlist 1
Prealgebra Lecture 2.5 Part 1: Order of Operations with Integers
From playlist Prealgebra Playlist 1
Prealgebra 1.4g - Ordering Numbers
Ordering numbers, and visualizing this order on a number line. Some very simple but extremely important ideas. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.
From playlist Prealgebra Chapter 1 (Complete chapter)
Jens Hemelaer - Toposes of presheaves on monoids as generalized topological spaces
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/HemelaerSlidesToposesOnline.pdf Various ideas from topology have been generalized to toposes, for example surjection
From playlist Toposes online
Petr Zograf - Enumeration of Grothendieck's dessins and KP hierarchy
Branched covers of the complex projective line ramified over 0,1 and infinity (Grothendieck's dessins d'enfant) of fixed genus and degree are effectively enumerated. More precisely, branched covers of a given ramification profile over infinity and given numbers of preimages
From playlist Physique mathématique des nombres de Hurwitz pour débutants
Can Wikipedia Help Offline Reinforcement Learning? (Paper Explained)
#wikipedia #reinforcementlearning #languagemodels Transformers have come to overtake many domain-targeted custom models in a wide variety of fields, such as Natural Language Processing, Computer Vision, Generative Modelling, and recently also Reinforcement Learning. This paper looks at th
From playlist Papers Explained
Binary Tree 3. Traverse (algorithms, pseudocode and VB.NET code)
This is the third in a series of videos about binary trees. It explains the differences between three depth first traversal strategies, namely pre order, in order and post order. It illustrates a simple method for determining the order in which data will be retrieved by each of these dept
From playlist Data Structures
Lars Thorge Jensen: Cellularity of the p-Kazhdan-Lusztig Basis for Symmetric Groups
After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the p-Kazhdan-Lusztig basis and give a complete description of p-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for p-
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Complex dynamics and arithmetic equidistribution – Laura DeMarco – ICM2018
Dynamical Systems and Ordinary Differential Equations Invited Lecture 9.5 Complex dynamics and arithmetic equidistribution Laura DeMarco Abstract: I will explain a notion of arithmetic equidistribution that has found application in the study of complex dynamical systems. It was first int
From playlist Dynamical Systems and ODE
Lecture 7: Hochschild homology in ∞-categories
In this video, we construct Hochschild homology in an arbitrary symmetric-monoidal ∞-category. The most important special case is the ∞-category of spectra, in which we get Topological Hochschild homology. Feel free to post comments and questions at our public forum at https://www.uni-mu
From playlist Topological Cyclic Homology
Category Theory 3.1: Examples of categories, orders, monoids
Examples of categories, orders, monoids.
From playlist Category Theory
The Axiom of Choice | Epic Math Time
The axiom of choice states that the cartesian product of nonempty sets is nonempty. This doesn't sound controversial, and it might not even sound interesting, but adopting the axiom of choice has far reaching consequences in mathematics, and applying it in proofs has a very distinctive qua
From playlist Latest Uploads
Prealgebra Lecture 2.5: Studying Order of Operations with Integers
https://www.patreon.com/ProfessorLeonard Prealgebra Lecture 2.5: Studying Order of Operations with Integers
From playlist Prealgebra (Full Length Videos)