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

Connected space and Simply connected space

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

Difference between Connected space and Simply connected space

Connected space vs. Simply connected space

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. In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

Similarities between Connected space and Simply connected space

Connected space and Simply connected space have 13 things in common (in Unionpedia): Connected space, Contractible space, Convex set, Covering space, Euclidean space, Genus (mathematics), Homotopy, Long line (topology), Manifold, N-connected space, Topological space, Topological vector space, Topology.

Connected space

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.

Connected space and Connected space · Connected space and Simply connected space · See more »

Contractible space

In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.

Connected space and Contractible space · Contractible space and Simply connected space · See more »

Convex set

In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.

Connected space and Convex set · Convex set and Simply connected space · See more »

Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

Connected space and Covering space · Covering space and Simply connected space · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Connected space and Euclidean space · Euclidean space and Simply connected space · See more »

Genus (mathematics)

In mathematics, genus (plural genera) has a few different, but closely related, meanings.

Connected space and Genus (mathematics) · Genus (mathematics) and Simply connected space · See more »

Homotopy

In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.

Connected space and Homotopy · Homotopy and Simply connected space · See more »

Long line (topology)

In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer".

Connected space and Long line (topology) · Long line (topology) and Simply connected space · See more »

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Connected space and Manifold · Manifold and Simply connected space · See more »

N-connected space

In the mathematical branch of algebraic topology, specifically homotopy theory, n-connectedness (sometimes, n-simple connectedness) generalizes the concepts of path-connectedness and simple connectedness.

Connected space and N-connected space · N-connected space and Simply connected space · 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.

Connected space and Topological space · Simply connected space and Topological space · See more »

Topological vector space

In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.

Connected space and Topological vector space · Simply connected space and Topological vector space · See more »

Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

Connected space and Topology · Simply connected space and Topology · See more »

The list above answers the following questions

Connected space and Simply connected space Comparison

Connected space has 77 relations, while Simply connected space has 44. As they have in common 13, the Jaccard index is 10.74% = 13 / (77 + 44).

References

This article shows the relationship between Connected space and Simply connected space. To access each article from which the information was extracted, please visit:

Hey! We are on Facebook now! »