Topology (disambiguation)
Encyclopedia
Topology
is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these properties are the topological invariants.
Topology may also refer to:
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these properties are the topological invariants.
Topology may also refer to:
- Topology, the collection of open sets used to define a topological spaceTopological spaceTopological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...
- Topology (journal)Topology (journal)Topology is a mathematical journal publishing scholarly articles related to topology and geometry. It was founded by J. H. C. Whitehead in 1962 and is published by Elsevier....
, a mathematical journal, with an emphasis on subject areas related to topology and geometry - Topology, a term used in architecture to describe spatial effects which cannot be described by topography, i.e., social, economical, spatial or phenomenological interactions
- Topology, a term used in cell biology to describe the specific orientationMembrane topologyIn biochemistry, the membrane topology of an transmembrane protein describes which portions of the amino-acid sequence of the protein lie within the plane of the surrounding lipid bilayer and which portions protrude into the watery environment on either side...
of transmembrane proteins. - Topology (electronics)Topology (electronics)The topology of an electronic circuit is the form taken by the network of interconnections of the circuit components. Different specific values or ratings of the components are regarded as being the same topology....
, a configuration of electronic components. - Network topologyNetwork topologyNetwork topology is the layout pattern of interconnections of the various elements of a computer or biological network....
, a term used to describe configurations of computer or biological networks. - Topology (musical ensemble)Topology (musical ensemble)Topology is a post-modernist quintet from Australia, formed in 1997. A leading Australian new music ensemble, they perform throughout Australia and abroad and have to date released four albums, including one with rock/electronica band Full Fathom Five and one with contemporary ensemble Loops. ...
, an Australian post-classical quintet - Geospatial topologyGeospatial topologyGeospatial topology studies the rules concerning the relationships between the points, lines, and polygons that represent the features of a geographic region. For example, where two polygons represent adjacent counties, typical topological rules would require that the counties share a common...
is the study or science of places with applications in earth scienceEarth scienceEarth science is an all-embracing term for the sciences related to the planet Earth. It is arguably a special case in planetary science, the Earth being the only known life-bearing planet. There are both reductionist and holistic approaches to Earth sciences...
, geographyGeographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...
, human geographyHuman geographyHuman geography is one of the two major sub-fields of the discipline of geography. Human geography is the study of the world, its people, communities, and cultures. Human geography differs from physical geography mainly in that it has a greater focus on studying human activities and is more...
, and geomorphologyGeomorphologyGeomorphology is the scientific study of landforms and the processes that shape them...
.- In geographic information systemGeographic Information SystemA geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...
s and their data structures, the terms "topologyGeospatial topologyGeospatial topology studies the rules concerning the relationships between the points, lines, and polygons that represent the features of a geographic region. For example, where two polygons represent adjacent counties, typical topological rules would require that the counties share a common...
" and "planar enforcement" are used to indicate that the border line between two neighboring areas (and the border point between two connecting lines) is stored only once. Thus, any rounding errors might move the border, but will not lead to gaps or overlaps between the areas. - Also in cartography, a topological mapTopological mapIn cartography and geology, a topological map is one that has been simplified so that only vital information remains and unnecessary detail has been removed. These maps lack scale, and distance and direction are subject to change and variation, but the relationship between points is maintained...
is a much simplified map that preserves the mathematical topology while sacrificing scale and shape - Topology is often confused with the geographic meaning of topographyTopographyTopography is the study of Earth's surface shape and features or those ofplanets, moons, and asteroids...
(originally the study of places). The confusion may be a factor in topographies having become confused with terrainTerrainTerrain, or land relief, is the vertical and horizontal dimension of land surface. When relief is described underwater, the term bathymetry is used...
or relief, such that they are essentially synonymous.
- In geographic information system
- In phylogeneticsPhylogeneticsIn biology, phylogenetics is the study of evolutionary relatedness among groups of organisms , which is discovered through molecular sequencing data and morphological data matrices...
, the branching pattern of a phylogenetic tree. - TopologiLinuxTopologilinuxTopologiLinux is a free Linux distribution to be run on or inside an existing Microsoft Windows system. The main feature of TopologiLinux is that it does not require any partitioning. It is based on Slackware and coLinux...
, a Linux distribution