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searching for Topological property 25 found (46 total)

Assortative mixing (607 words) [view diff] exact match in snippet view article find links to article

degree, and similarly for low degree. Because degree is itself a topological property of networks, this type of assortative mixing gives rise to more complex

Whitehead theorem (601 words) [view diff] exact match in snippet view article find links to article

algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping. In more detail, let X and Y be topological spaces.

Superhelix (314 words) [view diff] exact match in snippet view article find links to article

global geometry of a closed space curve. Contrary to intuition, a topological property, the linking number, arises from the geometric properties twist and

Nielsen–Olesen vortex (237 words) [view diff] exact match in snippet view article find links to article

in the configuration space. A configuration with this non-trivial topological property is called the Nielsen–Olesen vortex, after Holger Bech Nielsen and

Topology (chemistry) (375 words) [view diff] exact match in snippet view article

biological molecules achieve their activity. Circuit topology is a topological property of folded linear polymers. It describes the arrangement of intra-chain

Closed graph theorem (functional analysis) (4,695 words) [view diff] exact match in snippet view article

result connecting the continuity of certain kinds of functions to a topological property of their graph. In its most elementary form, the closed graph theorem

Atoms in molecules (1,524 words) [view diff] exact match in snippet view article find links to article

charge density topology. QTAIM rests on the fact that the dominant topological property of the vast majority of electron density distributions is the presence

Cantor space (654 words) [view diff] exact match in snippet view article find links to article

bases consisting of clopen sets are homeomorphic to each other. The topological property of having a base consisting of clopen sets is sometimes known as

Real tree (1,575 words) [view diff] exact match in snippet view article find links to article

triangles are "zero-thin"). Real trees can also be characterised by a topological property. A metric space X{\displaystyle X} is a real tree if for any pair

Furstenberg's proof of the infinitude of primes (838 words) [view diff] exact match in snippet view article find links to article

by the first topological property, the set on the left-hand side cannot be closed. On the other hand, by the second topological property, the sets S(p

Locally connected space (3,030 words) [view diff] exact match in snippet view article find links to article

Euclidean metric, played a large role in clarifying the notion of a topological property and thus a topological space. However, whereas the structure of compact

Fixed point (mathematics) (1,643 words) [view diff] exact match in snippet view article

Compactness alone does not imply the FPP, and convexity is not even a topological property, so it makes sense to ask how to topologically characterize the FPP

Planar Riemann surface (5,211 words) [view diff] exact match in snippet view article find links to article

open subset of the Riemann sphere. They are characterized by the topological property that the complement of every closed Jordan curve in the Riemann surface

Completely metrizable space (749 words) [view diff] exact match in snippet view article find links to article

subcategory of the category of metric spaces). Complete metrizability is a topological property while completeness is a property of the metric. The space (0,1) ⊂

Fixed-point property (660 words) [view diff] exact match in snippet view article find links to article

Compactness alone does not imply the FPP and convexity is not even a topological property so it makes sense to ask how to topologically characterize the FPP

Expansive homeomorphism (482 words) [view diff] exact match in snippet view article find links to article

assumed to be compact, since under that assumption expansivity is a topological property; i.e. if d′{\displaystyle d'} is any other metric generating the

Stanley–Reisner ring (1,343 words) [view diff] exact match in snippet view article find links to article

Munkres then shows that the Cohen–Macaulayness of Δ over k is a topological property: it depends only on the homeomorphism class of the simplicial complex

Distrontium ruthenate (1,476 words) [view diff] exact match in snippet view article find links to article

correct: the magnitude of edge current is not directly related to the topological property of the chiral state. In particular, although the non-trivial topology

Set theory (5,014 words) [view diff] exact match in snippet view article find links to article

determined often implies that a broader class of sets will have a topological property. The axiom of determinacy (AD) is an important object of study; although

Compact space (5,681 words) [view diff] exact match in snippet view article find links to article

{\displaystyle K\subseteq \bigcup _{S\in F}S\ .} Compactness is a topological property. That is, if K ⊂ Z ⊂ Y {\displaystyle K\subset Z\subset Y} , with

Kähler manifold (4,427 words) [view diff] exact match in snippet view article find links to article

independently by Buchdahl and Lamari. Thus "Kähler" is a purely topological property for compact complex surfaces. Hironaka's example shows, however,

Supermembranes (1,261 words) [view diff] exact match in snippet view article find links to article

if we associate somehow the coordinate of each particle with some topological property of the patches - perhaps holes in the membrane or closed loops. Since

Ricci flow (7,464 words) [view diff] exact match in snippet view article find links to article

n{\displaystyle n}-dimensional metric Riemannian manifold having a certain topological property (positive Euler characteristic), as the flow approaches some characteristic

Compactly generated space (4,588 words) [view diff] exact match in snippet view article find links to article

Proposition 1.6. Bankston, Paul (1979). "The total negation of a topological property". Illinois Journal of Mathematics. 23 (2): 241–252. doi:10.1215/ijm/1256048236

Selection principle (3,385 words) [view diff] exact match in snippet view article find links to article

Hurewicz's reformulation of Menger's property was the first important topological property described by a selection principle. Let A{\displaystyle \mathbf {A}