Point finite collection

Point finite collection

In mathematics, a collection mathcal{U} of subsets of a topological space X is said to be point finite or a point finite collection if every point of X lies in only finitely many members of mathcal{U}. Compare this to the stronger property of being locally finite. Point-finiteness is used in the definition of a metacompact space.

ee also

*Locally finite collection
*Metacompact space
*Paracompact space


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Locally finite collection — In the mathematical field of topology, local finiteness is a property of collections of subsets of a topological space. It is fundamental in the study of paracompactness and topological dimension. A collection of subsets of a topological space X… …   Wikipedia

  • Point process — In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces. For example, the occurrence …   Wikipedia

  • Finite intersection property — In general topology, the finite intersection property is a property of a collection of subsets of a set X . A collection has this property if the intersection over any finite subcollection of the collection is nonempty.DefinitionLet X be a set… …   Wikipedia

  • Finite geometry — A finite geometry is any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact precisely the same number of points as there are… …   Wikipedia

  • Finite potential barrier (QM) — In quantum mechanics, the finite potential barrier is a standard one dimensional problem that demonstrates the phenomenon of quantum tunnelling. The problem consists of solving the time independent Schrödinger equation for a particle with a… …   Wikipedia

  • Locally discrete collection — In mathematics, particularly topology, collections of subsets are said to be locally discrete if they look like they have precisely one element from a local point of view. The study of locally discrete collections is worthwile as Bing s… …   Wikipedia

  • Quantum finite automata — In quantum computing, quantum finite automata or QFA are a quantum analog of probabilistic automata. They are related to quantum computers in a similar fashion as finite automata are related to Turing machines. Several types of automata may be… …   Wikipedia

  • Particular point topology — In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and… …   Wikipedia

  • Floating point — In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent …   Wikipedia

  • Classification of finite simple groups — Group theory Group theory …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”