In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n-dimensional Euclidean space Rn, (n − 1)-dimensional spheres (that is, the boundaries of n-dimensional balls) have dimension n − 1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets. The small and large inductive dimensions are two of the three most usual ways of capturing the notion of "dimension" for a topological space, in a way that depends only on the topology (and not, say, on the properties of a metric space). The other is the Lebesgue covering dimension. The term "topological dimension" is ordinarily understood to refer to the Lebesgue covering dimension. For "sufficiently nice" spaces, the three measures of dimension are equal. (Wikipedia).
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
Introducing Infinity | Set Theory, Section 3.1
In this video we define inductive sets, the natural numbers, the axiom of infinity, and the standard order relation on the natural numbers. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Defining Natural Numbers as Sets (1:19) Definition of Inductive Sets (5:07) The Axiom o
From playlist Axiomatic Set Theory
Toy Ind3 - Part 02 - Indeterminacy Diagrams
This is terminology introduced to clarify the part of what goes on in IUT3. This isn't really in the body and Mochizuki may view this as implicit. We give an abstract definition of what an indeterminacy diagram is. We will apply this to the Log-Kummer correspondence. Errata: *The maps g
From playlist Toy Ind3
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
What is an equilateral triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Jennifer WILSON - High dimensional cohomology of SL_n(Z) and its principal congruence subgroups 3
Group cohomology of arithmetic groups is ubiquitous in the study of arithmetic K-theory and algebraic number theory. Rationally, SL_n(Z) and its finite index subgroups don't have cohomology above dimension n choose 2. Using Borel-Serre duality, one has access to the high dimensions. Church
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Transcience for the interchange process in dimension 5 - Allan Sly
Probability Seminar Topic: Transcience for the interchange process in dimension 5 Speaker: Allan Sly Affiliation: Princeton University Date: October 07, 2022 The interchange process \sigma_T is a random permutation valued process on a graph evolving in time by transpositions on its edge
From playlist Mathematics
Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek
Analysis & Mathematical Physics Topic: Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal Uncertainty Principle Speaker: Laura Cladek Affiliation: von Neumann Fellow, School Of Mathematics Date: December 14, 2022 We obtain new bounds on the additive energy
From playlist Mathematics
What do physicists mean by dimensions of space?
The 3 dimensions of our daily experience may be obvious, but a “dimension” means something specific to physicists. Brian Greene explains that meaning. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Fac
From playlist Science Unplugged: Extra Dimensions
Modular Representations of GL_n and Tensor Products of Galois Representations by Christophe Breuil
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last ye
From playlist Recent Developments Around P-adic Modular Forms (Online)
The top-heavy conjecture for vectors and matroids - Tom Braden
Members’ Seminar Topic: The top-heavy conjecture for vectors and matroids Speaker: Tom Braden SPEAKER AFFILIATION Affiliation: University of Massachusetts, Amherst; Member, School of Mathematics Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
8ECM Invited Lecture: Stuart White
From playlist 8ECM Invited Lectures
Introductory courses on Arthur packets 6
Wee Teck Gan National University of Singapore, Singapore Hiraku Atobe Hokkaido University, Japan
From playlist Introduction courses to Arthur packets
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
What is an equiangular triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties