Topology glossary
Topology glossary This is a glossary of some ... in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric topology. See ...
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Box topology
Box topology In topology, the cartesian product of topological spaces can ... topologies. The canonical one is the product topology, because it fits rather nicely with the ... a product. Another possibility is the box topology. The box topology has a somewhat more obvious definition ...
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Product topology
Product topology In topology and related areas of mathematics, a product ... of topological spaces equipped with a natural topology called the product topology. Definition Let I be a (possibly infinite ... i : X → X i . The product topology on X is defined to be ...
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Base (topology)
Base (topology) In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets ... We say that the base generates the topology T. Bases are useful because many properties ... to statements about a base generating that topology, and because many topologies are most easily ... it is not a base for any topology on X. (It is a subbase, ...
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Mackey topology
Mackey topology In functional analysis and related areas of mathematics the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still ... continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. The Mackey topology is the opposite ...
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Strong topology
Strong topology In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different ... context, and it may refer to: the topology arising from a norm the strong ...
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Order topology
Order topology In mathematics, the order topology is a topology that can be defined on any totally ... It is a natural generalization of the topology of the real numbers to arbitrary totally ... is a totally ordered set, the order topology on X is generated by the ...
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Discreet topology   (translated from Spanish)
Discreet topology discreet topology in a set X it is topología ... it is conjunto opened in the discreet topology. A space that has the discreet topology also knows like discreet space. The discreet topology is the topology finer than it ...
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Topology quotient   (translated from Italian)
Topology quotient In topologia , topology quotient it is intuitivamente that one obtained ... of equivalence on X. We define one topology onentirety quotient X/ ~ (that it consists of ... its class. We list to some definitions topology equivalents quotient on together X/~: With in ... its controimmagine through q in X. The topology on X/ ~ it is finer between ...
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Talk:Initial topology
Talk:Initial topology Coarsest topology I removed the following from the examples ... on a fixed set X the initial topology on X with respect to the functions ... topologies on X. That is, the initial topology τ is the topology generated by the union of the ...
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