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...urface mapping of the results of a [[fibre tracking]] study in which the [[topology]] of the [[cortical connectivity]] network in early [[blindness|blind]] sub

(of a set) In geometry and topology, a point such that every neighbourhood contains both points in the set and

In [[topology]], a '''limit point''' of a [[subset]] ''S'' of a topological space ''X'' i * The [[closure (topology)|closure]] of a set ''S'' is the union of ''S'' with its limit points.

...nternet Protocol networking, a '''stub network''' is a part of the network topology that can be used to reach hosts local to it, not other networks. A very si The first topology diagram shows a pair of broadcast-capable stub networks (e.g., Ethernet/IEE

...affic may traverse a path), these routing protocols need to apply not just topology and link metrics, but also the additional MPLS information that is used to ...packet-switching networks, but additional technologies, for which similar topology computation will work, such as optical wavelength and time division (e.g.,

...are useful in defining the [[algebraic fundamental group]] and the [[étale topology]]. The category of étale <math>S</math>-schemes becomes a [[Grothendieck topology]], if one defines the sets of coverings to be jointly-surjective collection

In geometry and topology, a point of a set which is not in the set and is not a [[boundary point]].

...d induces a [[topological space|topology]] in the set called the <i>metric topology</i>. == Metric topology ==

;: [[Neighborhood (topology)]]

...''n''(''r'') (that depends on the value of ''r'') of [[metric space#Metric topology|open balls]] of radius ''r'', <math>B_r(x_1),\ldots,B_r(x_{n(r)})\,</math>, ...[[complete metric space]] is totally bounded if and only if its [[closure (topology)|closure]] is [[compact space|compact]].

The '''topology''' of a [[computer network]] defines how that network is "laid out." Topolo ==Star topology==

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In [[topology]], a '''connected space''' is a [[topological space]] in which there is no * The connected subsets of the [[real number]]s with the Euclidean metric topology are the [[interval]]s.

In [[geometry]] and, more generally, in [[topology]], such that in every [[neighbourhood (topology)|neighbourhood]] there are points

...es of [[topological space]] according to how well the [[open set]]s of the topology distinguish between distinct points. ...''V'' are ''separated'' in ''X'' if ''U'' is disjoint from the [[Closure (topology)|closure]] of ''V'' and ''V'' is disjoint from the closure of ''U''.

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...called the <i>open sets</i> or the <i>topology</i> of <math>X</math>. The topology of <math>X</math> introduces an abstract structure of space in the set <mat ...imply write <math>X</math> instead of <math>(X,\mathcal T)</math> once the topology <math>\mathcal T</math> is established.

In [[general topology]], an '''open map''' is a [[function (mathematics)|function]] on a [[topolo ...cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=90 }}

In [[algebraic geometry]], [[differential geometry]], and [[differential topology]] the canonical sheaf is the top [[wedge product]] of the [[cotangent sheaf

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...to determine the best paths to other destinations from their place in the topology. Larger link state networks, for performance reasons, are usually hierarchi

...athematics for physicists and other outsiders: An introduction to algebra, topology, and functional analysis ...athematics for physicists and other outsiders: An introduction to algebra, topology, and functional analysis

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The '''Morita conjectures''' in [[topology]] ask .... Balogh, Non-shrinking open covers and K. Morita's duality conjectures, ''Topology Appl.'', '''115''' (2001) 333-341</ref>.

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...be '''dense''' in ''X'', or to be a dense set in ''X'', if the [[closure (topology)|closure]] of ''A'' coincides with ''X'' (that is, if <math>\scriptstyle \o ...ous functions]] on the interval [''a'',''b''] (with respect to the uniform topology).

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In [[topology]] for two topological spaces <math>X</math> and <math>Y</math> two continuo

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==Topology==

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In [[network topology]], a '''bus''' is a medium that is physically shared, or uses interconnecti

Auto-populated based on [[Special:WhatLinksHere/Quotient topology]]. Needs checking by a human.

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...ce is again a Banach space when it is endowed with the [[topological space|topology]] induced by the operator norm. If ''X'' is a Banach space then its dual sp ...X \rightarrow \,F</math> when ''F'' is endowed with the standard Euclidean topology.

The notion of a '''Grothendieck topology''' or '''site'''' captures the essential properties necessary for construct A ''Grothendieck topology'' <math>T</math> consists of

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...| first=John L. | last=Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | series=The University Series in Hig

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...table set|countably]] many copies of a two-point space with the [[discrete topology]]. It is thus [[compact space|compact]]. It may be realised as the space The topology on the countable product of the two-point space ''D'' is induced by the met

...It's true in a sense that CT is more general than algebra, as it includes topology, for example. But it treats it in an algebraic way, so I think it tends to ::Where is topology on the list, anyway? Can't see that anywhere either, fairly major branch.

* http://tools.ietf.org/html/rfc5120 Multi-Topology ISIS

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Network media have [[network topology|network topologies]] ranging from simple point-to-point to the any-to-any e

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In October 2007 the press announced the first issue of the ''Journal of Topology,'' published on behalf of the [[London Mathematical Society]].

In [[topology]] a surface is defined as a topological space such that * every point has a [[neighbourhood (topology)|neighbourhood]] that is homeomorphic to the (open) unit disk in <math>\mat

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* The complement of the closure of a set in ''X'' is the [[interior (topology)|interior]] of the complement of that set; the complement of the interior o

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...the open sets of <math>X</math> (or, equivalently, the [[topological space|topology]] of <math>X</math>). Then <math>A \subset X </math> is a Borel set of <mat

==Generic multicast topology== ...routers, need to share location information. This means that the multicast topology will need to be of a tree, with routers at the nodes and receiving hosts at

...], for example the algebra of the real numbers with the standard Euclidean topology. Countable additivity roughly means that the function assigns to any set ''

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In [[topology]], a '''neighbourhood of a point''' is any set that belongs to the '''neigh and define the topology induced by the metric.

In [[topology]], a '''neighbourhood of a point''' is any set that belongs to the '''neigh and define the topology induced by the metric.

==Topology==

...iven set which has properties generalising those of [[neighbourhood]] in [[topology]].

...y [[compact space|compact topological space]]s is compact in the [[product topology]].

...p;|&thinsp;''x''&nbsp;&minus;&nbsp;''y''&thinsp;|, and this yields a third topology on <math>\mathbb{Q}</math>. All three topologies coincide and turn the rati ...totally disconnected]]. The rational numbers do not form a [[completeness (topology)|complete metric space]]; the [[real numbers]] are the completion of <math>

In [[general topology]], an '''end''' of a [[topological space]] generalises the notion of "point

...rthur Steen | coauthors= J. Arthur Seebach jr | title=[[Counterexamples in Topology]] | year=1978 | publisher=[[Springer-Verlag]] | location=Berlin, New York |

...ausdorff space]] where each point has an [[open set|open]] [[neighborhood (topology)|neighborhood]] which is [[homeomorphism|homeomorphic]] to <math>\scriptsty

...less). With regards to IPv6 support, note that ISIS supports both "Single Topology (Single-SPF, multi-protocol)" as well as "MultiTopology (Multi-SPF, single

...'Physics, Topology, Logic and Computation: A Rosetta Stone''<ref> Physics, topology, logic and compIn New Structures for Physics, ed. Bob Coecke, Lecture Notes

In [[general topology]], the important property of '''[[compact set|compactness]]''' has a number

...d repeating signals so that the soldiers are in a full mesh. With the mesh topology, if terrain or construction masks the path between two radios, those soldie

...s a human activity, the theory of uniform spaces is a chapter of [[general topology]]. From the formal point of view, the notion of a uniform space is a siblin ...es that the reader is familiar with certain elementary, basic notions of [[topology]], namely:

...modulo the ideal generated by the polynomials in question. The [[Zariski topology]] (together with a structural sheaf of rings) on this set endows a geometri

...hout mathematics, and is encountered in the theory of [[metric space]]s in topology, the theory of [[normed vector space]]s in functional analysis, and in part

...[[closed set]]s in a [[topological space]]. The corresponding [[closure (topology)|closure operator]] is denoted <math>\overline A</math>. It may also be ob

An intelligent SBC, in the right topology, can considerably speed the processing of calls in the same part of the IP

...detect router failures. Database description are means of initializing the topology information. ...bout topology changes, both announcement and withdrawal of elements of the topology.

...use a physical (e.g., dialup) or logical (e.g., point-to-point over LANs) topology.<ref name=RFC1661>{{citation