Trees (topology) | Continuum theory
In mathematics, a dendroid is a type of topological space, satisfying the properties that it is hereditarily unicoherent (meaning that every subcontinuum of X is unicoherent), arcwise connected, and forms a continuum. The term dendroid was introduced by Bronisław Knaster lecturing at the University of Wrocław, although these spaces were studied earlier by Karol Borsuk and others. proved that dendroids have the fixed-point property: Every continuous function from a dendroid to itself has a fixed point. proved that every dendroid is tree-like, meaning that it has arbitrarily fine open covers whose nerve is a tree. The more general question of whether every tree-like continuum has the fixed-point property, posed by ,was solved in the negative by David P. Bellamy, who gave an example of a tree-like continuum without the fixed-point property. In Knaster's original publication on dendroids, in 1961, he posed the problem of characterizing the dendroids which can be embedded into the Euclidean plane. This problem remains open. Another problem posed in the same year by Knaster, on the existence of an uncountable collection of dendroids with the property that no dendroid in the collection has a continuous surjection onto any other dendroid in the collection, was solved by and , who gave an example of such a family. A locally connected dendroid is called a dendrite. A cone over the Cantor set (called a Cantor fan) is an example of a dendroid that is not a dendrite. (Wikipedia).
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
Ieke Moerdijk: An Introduction to Dendroidal Topology
Talk by Ieke Moerdijk in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/an-introduction-to-dendroidal-topology/ on April 23, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Eric Hoffbeck: Shuffles of trees
Abstract: We study a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. Our notion of shuffle is motivated by the theory of operads and occurs in the theory of dendroidal sets. We give several equivalent descriptions of the shuffles, and prove
From playlist Topology
Tashi Walde: 2-Segal spaces as invertible infinity-operads
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: We sketch the theory of (infinity-)operads via Segal dendroidal objects (due to Cisinski, Moerdijk and Weiss). We explain its relationship with the theory
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Sites/Coverings part 2: Grothendieck Topologies
Definition of a Grothendieck topology. This is just the axiomatization of coverings.
From playlist Sites, Coverings and Grothendieck Topologies
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
What Is Network Topology? | Types of Network Topology | BUS, RING, STAR, TREE, MESH | Simplilearn
In this video on Network Topology, we will understand What is Network topology, the role of using topology while designing a network, Different types of Topologies in a Network. Network topology provides us with a way to configure the most optimum network design according to our requiremen
From playlist Cyber Security Playlist [2023 Updated]🔥
Topology 1.4 : Product Topology Introduction
In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
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
What is a Manifold? Lesson 1: Point Set Topology and Topological Spaces
This will begin a short diversion into the subject of manifolds. I will review some point set topology and then discuss topological manifolds. Then I will return to the "What is a Tensor" series. It has been well over a year since we began this project. We now have a Patreon Page: https
From playlist What is a Manifold?
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
Classical and Digital Topological Groups
A research talk presented at the Fairfield University Mathematics Research Seminar, October 6, 2022. Should be accessible to a general mathematics audience, combining ideas from topology, graph theory, and abstract algebra. The paper is by me and Dae Woong Lee, available here: https://arx
From playlist Research & conference talks
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
What is a Manifold? Lesson 3: Separation
He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.
From playlist What is a Manifold?
An Introduction to Topological Spaces [Lori Ziegelmeier]
This tutorial provides an introduction to topological spaces, including a brief overview of some of the central mathematicians to define a topology. The primary focus is on the set of the real line with various notions of topologies defined on this set. This tutorial was contributed as pa
From playlist Tutorial-a-thon 2021 Spring
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology