Definition of topologies Topologies

We found 3 definitions of topologies from 2 different sources.

What does topologies mean?

Wiktionary

topologies (Noun)
Plural of topology.

Part of speech

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topologies, noun, plural of topology.

WordNet

Noun Plural: topologies
topology - the configuration of a communication network
		network topology
		configuration, constellation an arrangement of parts or elements; "the outcome depends on the configuration of influences at the time"
		bus topology, bus the topology of a network whose components are connected by a busbar
		loop topology, loop the topology of a network whose components are serially connected in such a way that the last component is connected to the first component
		star topology, star the topology of a network whose components are connected to a hub
		mesh topology, mesh the topology of a network whose components are all connected directly to every other component
		physical topology the appearance of the network; "the physical topologies of local area networks include the bus, the ring and the star"
topology - 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
		analysis situs
		pure mathematics the branches of mathematics that study and develop the principles of mathematics for their own sake rather than for their immediate usefulness
topology - 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"
topology - 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
		regional anatomy, topographic anatomy

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Wiktionary

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 τ of subsets of a set X such that the empty set and X are both members of τ and τ 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)
The topographical study of geographic locations or given places in relation to its history.
topology (Noun)
The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

Webster DictionaryWebster's Unabridged Dictionary 📘

topology (n.)
The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

OmegaWiki DictionaryOmegaWiki Dictionary Ω

topology
A branch of mathematics concerned with spatial properties preserved under bicontinuous deformation.
topology
The layout pattern of interconnections of the various elements (links, nodes, etc.) of a computer network.

Chambers DictionaryChamber's 20th Century Dictionary 📕

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

Wikipedia

Topology is the study of how spaces are organized, how the objects are structured in terms of position. It also studies how spaces are connected. It is divided into "algebraic topology", "differential topology" and "geometric topology".

Topology has sometimes been called rubber-sheet geometry, because in topology there is no difference between a circle and a square (a circle made out of a rubber band can be stretched into a square) but there is a difference between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing). The spaces studied in topology are called topological spaces. They vary from familiar manifolds to some very exotic constructions.

Natural Origin.

In many problems to solve, we often divide a large space into smaller areas, for instance, a house is divided into rooms, a nation into states, a type of quantity into numbers, etc. Each of these smaller areas (house, state, number) is adjacent to other small areas (other houses/states/numbers), the adjacencies between these spaces are connections. If we write down on paper a list of spaces, and the connections between them, we have written down a description of a space -- a topological space. All topological spaces have the same properties (adjacencies, etc.) and are made of the same structure (a list of smaller areas). Because of this, general algorithms and other forms of analysis are made possible. For instance, to program a robot to navigate a house, we simply give it a li