Topology - Wikipedia
Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing ...
Topology Definition & Meaning - Merriam-Webster
The meaning of TOPOLOGY is topographic study of a particular place; specifically : the history of a region as indicated by its topography. How to use topology in a sentence.
Topology | Types, Properties & Examples | Britannica
2024年11月21日 · topology, branch of mathematics, sometimes referred to as “rubber sheet geometry,” in which two objects are considered equivalent if they can be continuously deformed into one another through such motions in space as bending, twisting, stretching, and shrinking while disallowing tearing apart or gluing together parts.
Topology -- from Wolfram MathWorld
2024年12月18日 · Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid.
Introduction to Topology | Mathematics | MIT OpenCourseWare
This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such as function spaces, metrization theorems, embedding theorems and the fundamental group.
Topology: Definition, History, Types - OMC Math Blog
2024年3月29日 · Whether you were doing it to pass the time in the doctor’s office waiting room or to count how many different shapes you could make, this is actually what we call topology. Taking a shape and transforming it without breaking or having to reattach any corners or lines is exactly what topology is.
What is Topology? | Pure Mathematics - University of Waterloo
Topology studies properties of spaces that are invariant under any continuous deformation. It is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken.
(Discrete topology) The topology defined by T:= P(X) is called the discrete topology on X. (Finite complement topology) Define Tto be the collection of all subsets U of X such that X U either is finite or is all of X.
What is Topology? From Wikipedia \In mathematics, topology (from the Greek topos, ’place’, and logos, ’study’) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing." Intro to Topology R. L. Herman Spring ...
Topology | Brilliant Math & Science Wiki
Topology is the study of properties of geometric spaces which are preserved by continuous deformations (intuitively, stretching, rotating, or bending are continuous deformations; tearing or gluing are not). The theory originated as a way to classify and study properties of shapes in ...