Homotopy theory | Topological spaces | Categories in category theory | Topology
In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint. The distinguished point is just simply one particular point, picked out from the space, and given a name, such as that remains unchanged during subsequent discussion, and is kept track of during all operations. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e., a map between a pointed space with basepoint and a pointed space with basepoint is a based map if it is continuous with respect to the topologies of and and if This is usually denoted Pointed spaces are important in algebraic topology, particularly in homotopy theory, where many constructions, such as the fundamental group, depend on a choice of basepoint. The pointed set concept is less important; it is anyway the case of a pointed discrete space. Pointed spaces are often taken as a special case of the relative topology, where the subset is a single point. Thus, much of homotopy theory is usually developed on pointed spaces, and then moved to relative topologies in algebraic topology. (Wikipedia).
Name the segments in the given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Name the opposite rays in the given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Overview of points lines plans and their location
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Naming the rays in a given figure
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
What is a point a line and a plane
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
Learn how to apply a translation using a translation vector ex 2
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
CCSS How to Label a Line, Line Segment and Ray
π Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
What is a point line and plane
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
What is a Tensor 14: Vector and Tensor Fields
What is a Tensor 14: Vector and Tensor Fields
From playlist What is a Tensor?
Kohei Tanaka (10/20/22): Sectional category for maps of finite spaces
We consider the sectional category of a map between finite T_0 spaces (posets) from a combinatorial viewpoint. We compute some examples of the sectional category (or number) for the McCord map, the weak homotopy equivalence on the barycentric subdivision, and the Fadell-Neuwirth fibration
From playlist Topological Complexity Seminar
What is a Tensor 15: Coordinate Transformations
What is a Tensor 15: Coordinate Transformations
From playlist What is a Tensor?
Hyperbolic Graph Convolutional Networks | Geometric ML Paper Explained
β€οΈ Become The AI Epiphany Patreon β€οΈ https://www.patreon.com/theaiepiphany π¨βπ©βπ§βπ¦ Join our Discord community π¨βπ©βπ§βπ¦ https://discord.gg/peBrCpheKE In this video we dig deep into the hyperbolic graph convolutional networks paper introducing a class of GCNs operating in the hyperbolic spa
From playlist Graph Neural Nets
Parvaneh Joharinad (7/27/22): Curvature of data
Abstract: How can one determine the curvature of data and how does it help to derive the salient structural features of a data set? After determining the appropriate model to represent data, the next step is to derive the salient structural features of data based on the tools available for
From playlist Applied Geometry for Data Sciences 2022
What is a Tensor? Lesson 16: The metric tensor field
What is a Tensor? Lesson 16: The metric tensor field
From playlist What is a Tensor?
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
Topological Analysis of Grain Boundaries - Srikanth Patala
Srikanth Patala Masachusetts Institute of Technology February 1, 2011 GEOMETRY AND CELL COMPLEXES Polycrystalline materials, such as metals, ceramics and geological materials, are aggregates of single-crystal grains that are held together by highly defective boundaries. The structure of g
From playlist Mathematics
Diego MondΓ©jar Ruiz (6/10/22): Approximation of compact metric spaces by finite samples
We address the problem of reconstructing topological properties of a compact metric space by means of simpler ones. In this context, we use inverse sequences of finite topological spaces and polyhedra made from finite approximations of the space. This construction is related with Borsuk's
From playlist Vietoris-Rips Seminar
π Learn essential definitions of points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A plane contains infinite number of lines. A ray is a li
From playlist Points Lines and Planes
CS224W: Machine Learning with Graphs | 2021 | Lecture 19.2 - Hyperbolic Graph Embeddings
For more information about Stanfordβs Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Brc7vN Jure Leskovec Computer Science, PhD In previous lectures, we focused on graph representation learning in Euclidean embedding spaces. In this lecture, we in
From playlist Stanford CS224W: Machine Learning with Graphs