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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 Topologist's sine curve, a useful example in point-set topology.It is connected but not path-connected. In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. [1] [2] Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, [3] industrial fieldbusses and computer networks.
Topology of a bus network. A bus network is a network topology in which nodes are directly connected to a common half-duplex link called a bus. [1] [2]A conceptual diagram of a local area network using bus topology
The simplistic Jellyfish model of the World Wide Web centers around a large strongly connected core of high-degree web pages that form a clique; pages such that there is a path from any page within the core to any other page.
The new added bit should be ‘0’ for one 3D hypercube and ‘1’ for the other 3D hypercube. The corners of the respective one-bit changed MSBs are connected to create the higher hypercube network. This method can be used to construct any m-bit represented hypercube with (m-1)-bit represented hypercube.
Topological geometry deals with incidence structures consisting of a point set and a family of subsets of called lines or circles etc. such that both and carry a topology and all geometric operations like joining points by a line or intersecting lines are continuous.
In general topology and related areas of mathematics, the initial topology (or induced topology [1] [2] or strong topology or limit topology or projective topology) on a set, with respect to a family of functions on , is the coarsest topology on that makes those functions continuous.