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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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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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Talk:Final topology
Talk:Final topology Coarsest topology I'm removing the following from the ... on a fixed set X the final topology on X with respect to the functions ... topologies on X. That is, the final topology τ is the intersection of the topologies ... one is supposed to describe the initial topology not the final topology: The intersection ...
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Topological space
... spaces in their own right is called topology. This article is technical. For a general ... of the subject, see the article on topology. Definition A topological space is a set ... in T. The collection T is a topology on X. The sets in T are ... replaced by the equivalent one that the topology be closed under all finite intersections instead ... topological space. When every set in a topology T 1 is also in a ...
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Talk:Topological space
... that there can be more than one topology on a set? We wouldn't want people thinking the standard topology on R is the only one. Roughly ... well with me. The basic relation in topology isn't between points and other points ... you much (if any) information about the topology at all. For instance, in Euclidean space ... MANY uses of simple algebra. What is topology good for? I just think it ...
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Comparison of topologies
Comparison of topologies In topology and related areas of mathematics comparison of ... also open under τ 2 . Then the topology τ 1 is said to be a coarser (weaker or smaller) topology than τ 2 , and τ 2 is ... to be a finer (stronger or larger) topology than τ 1 . If additionally |
Category:Previous 168 years (translated from Chinese)
... a package of axiom. □thick develops □(Coarser topology). If X Is □is spatial □, also ... Tightly opens the analysis situs(Compact-open topology) Tests □possesses by X To Y □□the ... Tightly opens the analysis situs(compact-open topology): No matter what □one □ X □□subset ... to open the analysis situs (compact-open topology). □(Complete). If all tan oak ...
http://zh.wikipedia.org/wiki/拓撲學術語 - 62k - Cached (Chinese) - Wikipedia (Chinese) - Similar pages
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Order theory
... important in the study of universal algebra. Topology In topology orders play a very prominent role. In ... of sets can be used to define topology. Beyond these relations, topology can be looked at solely in terms ... which leads to the study of pointless topology. Furthermore, a natural preorder of elements ...
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Specialization (pre)order
... In the branch of mathematics known as topology, the specialization (or canonical) preorder defines a ... On the other hand, if the underlying topology is T 1 , then the specialization order ... sets are inaccessible by directed suprema. A topology is order consistent with respect to a ... to obtain a partial order from every topology. It is natural to ask for the ... obtained as a specialization order of some topology? Indeed, the answer to this question ...
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User talk:Prumpf
... Let G_ch be G with the chaotic topology (i.e. only G_ch and the empty ... Hausdorff, but I think considering the Bohr topology as a topology on G that might just fail to be Hausdorff rather than a topology on a quotient of G that always ... similar to G, but has a potentially coarser topology. I'm rather tempted to ...
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