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 | 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 Definition & Meaning - Merriam-Webster
2012年11月9日 · 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.
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.
Types of Network Topology - GeeksforGeeks
2024年11月19日 · Network topology refers to the arrangement of different elements like nodes, links, or devices in a computer network. Common types of network topology include bus, star, ring, mesh, and tree topologies, each with its advantages and disadvantages.
Topology -- from Wolfram MathWorld
2 天之前 · 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.
(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? | 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.
Topology 101: The Hole Truth - Quanta Magazine
2021年1月26日 · But to understand why – and why mathematicians even care about holes in the first place — we have to travel through the history of topology, starting with how it differs from its close kin, geometry.
Topology - Mathematics
Topology is a branch of mathematics that involves properties that are preserved by continuous transformations. In fact, a “topology” is precisely the minimum structure on a set that allows one to even define what “continuous” means.