topologytəˈpɒl ə dʒi
topology (n)
- plural
- topologies
English Definitions:
topology (noun)
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"
regional anatomy, topographic anatomy, topology (noun)
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
topology, analysis situs (noun)
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
topology, network topology (noun)
the configuration of a communication network
topology (Noun)
A branch of mathematics studying those properties of a geometric figure or solid that are not changed by stretching, bending and similar homeomorphisms.
topology (Noun)
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.
topology (Noun)
The anatomical structure of part of the body.
topology (Noun)
The arrangement of nodes in a communications network.
topology (Noun)
The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
topology (Noun)
(topography) The topographical study of geographic locations or given places in relation to its history.
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.
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.
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