• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
NONPOSITIVE CURVATURE AND REFLECTION GROUPS Michael
NONPOSITIVE CURVATURE AND REFLECTION GROUPS Michael

LOCAL HOMEOMORPHISMS VIA ULTRAFILTER
LOCAL HOMEOMORPHISMS VIA ULTRAFILTER

PowerPoint 演示文稿 - Welcome to Dr Wang Xingbo's Website
PowerPoint 演示文稿 - Welcome to Dr Wang Xingbo's Website

Shortest paths and geodesics
Shortest paths and geodesics

Repovš D.: Topology and Chaos
Repovš D.: Topology and Chaos

... If a continuous function is one-to-one and onto and if its inverse is also continuous, then the function is called a homeomorphism. If two spaces are homeomorphic, they have identical topological properties, and are considered to be topologically the same. ...
NOTES ON GENERAL TOPOLOGY 1. The notion of a topological
NOTES ON GENERAL TOPOLOGY 1. The notion of a topological

LOCAL HOMEOMORPHISMS VIA ULTRAFILTER CONVERGENCE
LOCAL HOMEOMORPHISMS VIA ULTRAFILTER CONVERGENCE

4a.pdf
4a.pdf

Manifolds of smooth maps
Manifolds of smooth maps

Math 396. Quotients by group actions Many important manifolds are
Math 396. Quotients by group actions Many important manifolds are

26 - HKU
26 - HKU

de Rham cohomology
de Rham cohomology

The bordism version of the h
The bordism version of the h

Mathematical Tools for 3D Shape Analysis and - imati-cnr
Mathematical Tools for 3D Shape Analysis and - imati-cnr

Introduction to weakly b- transitive maps on topological spaces
Introduction to weakly b- transitive maps on topological spaces

Classifying spaces for groupoid structures
Classifying spaces for groupoid structures

Tibor Macko
Tibor Macko

Quotient spaces
Quotient spaces

PDF
PDF

Sung-Hoon Park - Quotient Topology
Sung-Hoon Park - Quotient Topology

Solenoids
Solenoids

Completeness and quasi-completeness
Completeness and quasi-completeness

WHAT IS A TOPOLOGICAL STACK? 1. introduction Stacks were
WHAT IS A TOPOLOGICAL STACK? 1. introduction Stacks were

Unwinding and integration on quotients
Unwinding and integration on quotients

Math 396. Paracompactness and local compactness 1. Motivation
Math 396. Paracompactness and local compactness 1. Motivation

< 1 2 3 4 5 6 7 8 9 10 ... 17 >

Manifold



In mathematics, a manifold is a topological space that resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be embedded in three dimensional real space, but also the Klein bottle and real projective plane which cannot.Although a manifold resembles Euclidean space near each point, globally it may not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map.The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. One important class of manifolds is the class of differentiable manifolds.This differentiable structure allows calculus to be done on manifolds. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report