Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Free
Faster access than browser!
 

Base (topology) and Connected space

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Base (topology) and Connected space

Base (topology) vs. Connected space

In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set. In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

Similarities between Base (topology) and Connected space

Base (topology) and Connected space have 14 things in common (in Unionpedia): Closed set, Complement (set theory), Continuous function, Discrete space, If and only if, Interval (mathematics), Mathematics, Maximal and minimal elements, Open set, Product topology, Real line, Real number, Singleton (mathematics), Topological space.

Closed set

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.

Base (topology) and Closed set · Closed set and Connected space · See more »

Complement (set theory)

In set theory, the complement of a set refers to elements not in.

Base (topology) and Complement (set theory) · Complement (set theory) and Connected space · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

Base (topology) and Continuous function · Connected space and Continuous function · See more »

Discrete space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.

Base (topology) and Discrete space · Connected space and Discrete space · See more »

If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

Base (topology) and If and only if · Connected space and If and only if · See more »

Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

Base (topology) and Interval (mathematics) · Connected space and Interval (mathematics) · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Base (topology) and Mathematics · Connected space and Mathematics · See more »

Maximal and minimal elements

In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set (poset) is an element of S that is not smaller than any other element in S. A minimal element of a subset S of some partially ordered set is defined dually as an element of S that is not greater than any other element in S. The notions of maximal and minimal elements are weaker than those of greatest element and least element which are also known, respectively, as maximum and minimum.

Base (topology) and Maximal and minimal elements · Connected space and Maximal and minimal elements · See more »

Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

Base (topology) and Open set · Connected space and Open set · See more »

Product topology

In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.

Base (topology) and Product topology · Connected space and Product topology · See more »

Real line

In mathematics, the real line, or real number line is the line whose points are the real numbers.

Base (topology) and Real line · Connected space and Real line · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

Base (topology) and Real number · Connected space and Real number · See more »

Singleton (mathematics)

In mathematics, a singleton, also known as a unit set, is a set with exactly one element.

Base (topology) and Singleton (mathematics) · Connected space and Singleton (mathematics) · See more »

Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

Base (topology) and Topological space · Connected space and Topological space · See more »

The list above answers the following questions

Base (topology) and Connected space Comparison

Base (topology) has 36 relations, while Connected space has 77. As they have in common 14, the Jaccard index is 12.39% = 14 / (36 + 77).

References

This article shows the relationship between Base (topology) and Connected space. To access each article from which the information was extracted, please visit:

Hey! We are on Facebook now! »