What does topology mean?

Definitions for topology
təˈpɒl ə dʒitopol·o·gy

This dictionary definitions page includes all the possible meanings, example usage and translations of the word topology.

Princeton's WordNet

  1. topologynoun

    topographic study of a given place (especially the history of the place as indicated by its topography)

    "Greenland's topology has been shaped by the glaciers of the ice age"

  2. regional anatomy, topographic anatomy, topologynoun

    the study of anatomy based on regions or divisions of the body and emphasizing the relations between various structures (muscles and nerves and arteries etc.) in that region

  3. topology, analysis situsnoun

    the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions

  4. topology, network topologynoun

    the configuration of a communication network

Wiktionary

  1. topologynoun

    A branch of mathematics studying those properties of a geometric figure or solid that are not changed by stretching, bending and similar homeomorphisms.

  2. topologynoun

    A collection u03C4 of subsets of a set X such that the empty set and X are both members of u03C4 and u03C4 is closed under arbitrary unions and finite intersections.

  3. topologynoun

    The anatomical structure of part of the body.

  4. topologynoun

    The arrangement of nodes in a communications network.

  5. topologynoun

    The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.

  6. topologynoun

    (topography) The topographical study of geographic locations or given places in relation to its history.

Wikipedia

  1. Topology

    In mathematics, topology (from the Greek words τόπος, 'place, location' and λόγος, 'study') concerns 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 through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles. The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed.

ChatGPT

  1. topology

    A topology is a mathematical concept in set theory that abstractly defines the concepts of closeness, limit, continuity and convergence. It is a collection of open sets on a given set that satisfy the following properties: 1. The empty set and the given set itself are included in the collection. 2. Any union of open sets from the collection is also an open set (in other words, open sets are closed under arbitrary unions). 3. The intersection of any finite number of open sets is also an open set (open sets are closed under finite intersections). The set with the topology is called a topological space.

Webster Dictionary

  1. Topologynoun

    the art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place

Wikidata

  1. Topology

    Topology is the mathematical study of shapes and spaces. A major area of mathematics concerned with the most basic properties of space, such as connectedness, continuity and boundary. It is the study of properties that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. The exact mathematical definition is given below. Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, referred to in Latin as the geometria situs or analysis situs. This later acquired the name topology. By the middle of the 20th century, topology had become an important area of study within mathematics. Topology has many subfields. ⁕Point-set topology establishes the foundational aspects of topology and investigates concepts inherent to topological spaces. ⁕Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology and homotopy groups.

Chambers 20th Century Dictionary

  1. Topology

    tō-pol′ō-ji, n. the art of aiding the memory by associating things with places. [Gr. topos, a place, legein, to speak.]

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Numerology

  1. Chaldean Numerology

    The numerical value of topology in Chaldean Numerology is: 4

  2. Pythagorean Numerology

    The numerical value of topology in Pythagorean Numerology is: 8

Examples of topology in a Sentence

  1. Rainer Deutschmann:

    We will see on each journey what the energy consumption will be depending on the geography and topology, with an electric battery, instead of carrying merchandise around you are carrying around the battery. You have a 200 km range, which you can use for a city, but you cannot use it for the Alps.

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Translations for topology

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"topology." Definitions.net. STANDS4 LLC, 2024. Web. 15 Jun 2024. <https://www.definitions.net/definition/topology>.

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