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A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally in fields such as computational geometry, graphics, robotics, social science, structural biology, and chemistry, using methods from computable topology. [1] [2] [3]
Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates , or signal types may differ between two different networks, yet their logical ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. 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 ...
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property .
The Database of Original & Non-Theoretical Uses of Topology (DONUT) is a database of scholarly articles featuring practical applications of topological data analysis to various areas of science. DONUT was started in 2017 by Barbara Giunti, Janis Lazovskis, and Bastian Rieck, [ 126 ] and as of October 2023 currently contains 447 articles. [ 127 ]
The topology of λ-calculus is the Scott topology, and when restricted to continuous functions the type free λ-calculus amounts to a topological space reliant on the tree topology. Both the Scott and Tree topologies exhibit continuity with respect to the binary operators of application ( f applied to a = fa ) and abstraction ((λx.t(x))a = t(a ...
Digital topology was first studied in the late 1960s by the computer image analysis researcher Azriel Rosenfeld (1931–2004), whose publications on the subject played a major role in establishing and developing the field. The term "digital topology" was itself invented by Rosenfeld, who used it in a 1973 publication for the first time.
Star topology in use in a network. A star network is an implementation of a spoke–hub distribution paradigm in computer networks. In a star network, every host is connected to a central hub. In its simplest form, one central hub acts as a conduit to transmit messages. [1] The star network is one of the most common computer network topologies.