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In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
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]
The finest topology on X is the discrete topology; this topology makes all subsets open. The coarsest topology on X is the trivial topology; this topology only admits the empty set and the whole space as open sets. In function spaces and spaces of measures there are often a number of possible topologies.
In computer networking, hypercube networks are a type of network topology used to connect and route data between multiple processing units or computers. Hypercube networks consist of 2 m nodes, which form the vertices of squares to create an internetwork connection.
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 ...
The architecture uses commodity switches that are cheaper and more power-efficient than high-end modular data center switches. This topology is actually a special instance of a Clos network, rather than a fat-tree as described above. That is because the edges near the root are emulated by many links to separate parents instead of a single high ...
The ratio of switching nodes to processor nodes is greater than one in a butterfly network. Such topology, where the ratio of switching nodes to processor nodes is greater than one, is called an indirect topology. [1] The network derives its name from connections between nodes in two adjacent ranks (as shown in figure 1), which resembles a ...
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.