Topology (11069 bytes)
3: '''Topology''' ([[Greek language|Greek]] ''topos'' = place an...
5: Topology is concerned with the study of the so-called [[to...
14: ...y]] contains definitions of terms used throughout topology.
17: The root of topology was in the study of geometry in ancient cultures....
29: ...e status of the '''topologist''', a specialist in topology, was probably established from around 1920.

Chart (2232 bytes)
1: ...hart''' is a graphic representation of some data. Charts are often used to make large quantities of data ...
3: ...sented, for example, in a [[histogram]] (or [[bar chart]]).
5: ...can be created dynamically by computers using a [[charting application]].
7: Charts are not always used for mathematical purposes, b...
9: ==Examples of various charts==

General topology (2285 bytes)
1: ...' or '''point set topology''' is that branch of [[topology]] which studies elementary properties of [[topolo...
3: More specifically, it is in general topology that basic notions, such as:
8: * [[limit (topology)|convergence]] of [[sequence]]s, [[net (mathemati...
13: ...erential topology]]. As the name implies, general topology provides the common foundation for these areas.
15: ...r detailed definitions; and the [[list of general topology topics]].

Membrane topology (1684 bytes)
1: ...nt on either side. More succinictly, the membrane topology describes which regions of the polypeptide chain ...
3: ...icity]] of amino acids individually, the membrane topology of a protein (and indeed whether or not it is an ...
5: ...ein-coupled receptor|"7TM receptors"]]). Membrane topology predictions also can be invaluable for developing...

Order topology (1511 bytes)
1: ...red set]]. It is a natural generalization of the topology of the [[real numbers]] to arbitrary totally orde...
3: ...als form a [[base (topology)|base]] for the order topology.
5: Several interesting variants of the order topology can be given:
7: * The '''left order topology''' on ''X'' is the topology whose open sets consist of intervals of the form ...
8: * The '''right order topology''' on ''X'' is the topology whose open sets consist of intervals of the form ...

Boundary (topology) (2249 bytes)
3: ...losure (topology)|closure]] minus its [[interior (topology)|interior]]. An element of the boundary of ''S'' ...
8: ... boundary point of ''S'' if every [[neighborhood (topology)|neighborhood]] of ''p'' contains at least one p...
26: [[Category:General topology]]

Cone (topology) (2071 bytes)
1: In [[topology]], especially [[algebraic topology]], the '''cone''' ''CX'' '''of a [[topological sp...
5: of the [[product topology|product]] of ''X'' with the [[unit interval]] ''I...
6: ...nd collapse one end of the cylinder to a [[point (topology)|point]].
28: ...cisely because it embeds a space as a [[subspace (topology)|subspace]] of a contractible space.
32: *[[suspension (topology)]]

DNA topology (570 bytes)
1: ...s. [[Topoisomerase]]s are enzymes that change the topology of DNA.

Zariski topology (1750 bytes)
1: In [[mathematics]], the '''Zariski topology''' is a structure basic to [[algebraic geometry]]...
3: The Zariski [[topology]] is defined by defining the [[closed set]]s to b...
5: This is a topology because the intersection of any number of closed ...
9: ...inition above. That this definition yields a true topology is easily verified.
13: The Zariski topology given to some finite-dimensional vector space doe...

Point (topology) (160 bytes)
1: [[Category:Topology]]
2: In [[mathematics]], particularly in [[topology]], a [[point]] of a [[topological space]] is an e...

Trivial topology (4130 bytes)
1: ...gy]], a [[topological space]] with the '''trivial topology''' is one where the only [[open set]]s are the [[...
3: ...r> with more than [[one]] element and the trivial topology lacks a key desirable property: it is not a [[T0 ...
8: * The only possible [[basis (topology)|basis]] of <var>X</var> is {<var>X</var>}.
11: * Not being Hausdorff, ''X'' is not an [[order topology]], nor is it [[metrizable]].
16: ...ogy)|subspace]]s of <var>X</var> have the trivial topology.

Strong topology (472 bytes)
1: ...ogy]] which is stronger than some other "default" topology. This term is used to describe different topologi...
2: * the topology arising from a [[normed vector space|norm]]
3: * the [[strong operator topology]]
5: ...is stronger than a topology &sigma; (is a [[finer topology]]) if it contains more [[open set]]s.
8: * [[weak topology]]

Finer topology (1785 bytes)
1: ...oarser''' (alt. '''weaker''' or '''smaller''') '''topology''' than &tau;₁.
5: ...>) to (''X'',&tau;₂), is [[continuity (topology)|continuous]]. If &tau;₁ is the finer ...
7: ... The coarsest topology on ''X'' is the [[trivial topology]]. Any two topologies on ''X'' have a ''meet'' an...
12: *[[Weak topology]]
13: *[[Strong topology]]

Alexandrov topology (13413 bytes)
1: In [[general topology]] the open sets of a [[topological space]] satisf...
6: ...sets is open?"'' The answer is, the '''Alexandrov topology'''.
29: ...ization preorder]] of '''''X''''' i.e. the finest topology giving the preorder &le; satisfying ''x'' &le; ''...
37: ...subspace characterization.''' ''T'' is the finest topology consistent with the topologies of the finite subs...
41: ... their topology ''T'' is called the '''Alexandrov topology''', named after the Russian mathematician [[Pavel...

Geometric topology (1821 bytes)
1: ...e to be almost synonymous with '''low-dimensional topology''', concerning in particular objects of two, thre...
3: ...l technique. These fields all rested on [[general topology]], which was the study of the general [[topologic...
5: The methods of geometric topology being combinatorial, and difficulties arising (fo...
7: ...ainly broke down the barriers with other parts of topology and geometry, making the subject more part of the...
9: See also: [[list of geometric topology topics]]

Fork (topology) (1319 bytes)
1: ...aracterization of [[graph]]s, including [[network topology]], and [[topological space]]s.
5: ...e [[Glossary of graph theory#Graph topology|graph topology]] of a graph with a fork.
6: Stated in terms of [[topology]] alone, a topological space ''X'' has a fork if ...

Cover (topology) (2566 bytes)
7: ...;</sub> is contained in ''T'', where ''T'' is the topology on ''X'').
15: ...''' if every point of ''X'' has a [[neighborhood (topology)|neighborhood]] which intersects only [[finite]]l...
30: *[[atlas (topology)]]
32: [[Category:Topology|Cover]]
33: [[Category:General topology|Cover]]

Logical topology (682 bytes)
1: ...ogical Topology''' (also referred to as '''Signal Topology''') is a network computing term used to describe ...
3: ...tructure of the network, is called the [[physical topology]].
8: ...The [[Ethernet]] protocol is a common logical bus topology protocol
9: * [[LocalTalk]] is a common logical bus or star topology protocol
10: * [[Token Ring]] is a common logical ring topology protocol

Continuity (topology) (3981 bytes)
1: [[Category:Topology]][[Category:General topology]]
2: In [[topology]], a '''continuous''' function is generally defin...
9: ...e <math>x \in X</math> if for any [[neighborhood (topology)|neighborhood]] <var>V</var> of <var>f</var>(<var...
11: <center>[[image:continuity_topology.png|Continuity of a function at a point]]</center...
29: ...uous. If the domain set is given the [[indiscrete topology]] and the range set is at least [[T0 space|T<sub>...

Noncommutative topology (754 bytes)
1: ...origins in the [[Gel'fand duality]] between the [[topology]] of [[locally compact]] spaces and the [[algebra...

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