Cover (topology), the Glossary

Table of Contents

1. 31 relations: Čech cohomology, Barycentric subdivision, Compact space, Countable set, Family of sets, Finite set, Indexed family, Interval (mathematics), John L. Kelley, Lebesgue covering dimension, Lindelöf space, Locally finite collection, Mathematics, Metacompact space, Neighbourhood (mathematics), Open set, Paracompact space, Prentice Hall, Real coordinate space, Reflexive relation, Set (mathematics), Set theory, Simplex, Simplicial complex, Star refinement, Subset, Symmetric relation, Topological space, Topology, Transitive relation, Trivial topology.

Čech cohomology

In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space.

See Cover (topology) and Čech cohomology

Barycentric subdivision

In mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones.

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Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. Cover (topology) and compact space are general topology and topology.

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Countable set

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers.

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Family of sets

In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. Cover (topology) and family of sets are Families of sets.

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Finite set

In mathematics, particularly set theory, a finite set is a set that has a finite number of elements.

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Indexed family

In mathematics, a family, or indexed family, is informally a collection of objects, each associated with an index from some index set.

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Interval (mathematics)

In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Cover (topology) and interval (mathematics) are topology.

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John L. Kelley

John L. Kelley (December 6, 1916, Kansas – November 26, 1999, Berkeley, California) was an American mathematician at the University of California, Berkeley, who worked in general topology and functional analysis.

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Lebesgue covering dimension

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.

See Cover (topology) and Lebesgue covering dimension

Lindelöf space

In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. Cover (topology) and Lindelöf space are general topology.

See Cover (topology) and Lindelöf space

Locally finite collection

A collection of subsets of a topological space X is said to be locally finite if each point in the space has a neighbourhood that intersects only finitely many of the sets in the collection. Cover (topology) and locally finite collection are Families of sets and general topology.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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In the mathematical field of general topology, a topological space is said to be metacompact if every open cover has a point-finite open refinement.

See Cover (topology) and Metacompact space

Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Cover (topology) and neighbourhood (mathematics) are general topology.

See Cover (topology) and Neighbourhood (mathematics)

Open set

In mathematics, an open set is a generalization of an open interval in the real line. Cover (topology) and open set are general topology.

See Cover (topology) and Open set

Paracompact space

In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite.

See Cover (topology) and Paracompact space

Prentice Hall

Prentice Hall was a major American educational publisher.

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Real coordinate space

In mathematics, the real coordinate space or real coordinate n-space, of dimension, denoted or, is the set of all ordered n-tuples of real numbers, that is the set of all sequences of real numbers, also known as coordinate vectors.

See Cover (topology) and Real coordinate space

Reflexive relation

In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself.

See Cover (topology) and Reflexive relation

Set (mathematics)

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

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Set theory

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.

See Cover (topology) and Set theory

Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. Cover (topology) and simplex are topology.

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Simplicial complex

In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).

See Cover (topology) and Simplicial complex

Star refinement

In mathematics, specifically in the study of topology and open covers of a topological space X, a star refinement is a particular kind of refinement of an open cover of X. A related concept is the notion of barycentric refinement. Cover (topology) and star refinement are general topology.

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Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

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Symmetric relation

A symmetric relation is a type of binary relation.

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Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. Cover (topology) and topological space are general topology.

See Cover (topology) and Topological space

Topology

Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

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Transitive relation

In mathematics, a binary relation on a set is transitive if, for all elements,, in, whenever relates to and to, then also relates to.

See Cover (topology) and Transitive relation

Trivial topology

In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Cover (topology) and trivial topology are general topology and topology.

See Cover (topology) and Trivial topology

References

[1] https://en.wikipedia.org/wiki/Cover_(topology)

Also known as Cover (mathematics), Cover (set theory), Finite cover, Open cover, Open covering, Open coverings, Refinement (topology), Refinement of a cover, Refinement of an open cover, Subcover, Subcovering.