Connected and disconnected subspaces of R² In topology and related branches of mathematics, a connected space is a topological space that cannot be represented...

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...

uniformly connected space or Cantor connected space is a uniform space U such that every uniformly continuous function from U to a discrete uniform space is...

topological space X is locally connected if every point admits a neighbourhood basis consisting of open connected sets. As a stronger notion, the space X is...

2004 "Connected" (RBD song), 2006 "Connected" (Stereo MCs song), 1992 Connected space, a mathematical concept in topology Path-connected space Simply...

connected if, when it is considered as a topological space, it is a connected space. Thus, manifolds, Lie groups, and graphs are all called connected...

simply connected is a certain local connectedness condition that arises in the theory of covering spaces. Roughly speaking, a topological space X is semi-locally...

surjective in the case that X {\displaystyle X} is not connected. For every topological space X {\displaystyle X} , the identity map id : X → X {\displaystyle...

locally simply connected space is a topological space that admits a basis of simply connected sets. Every locally simply connected space is also locally...

connectivity is based on the homotopy groups of the space. A space is n-connected (or n-simple connected) if its first n homotopy groups are trivial. Homotopical...

both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces. Separated sets should...

connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space. Metric spaces...

space Lindelöf space Sigma-compact space Connected space T0 space T1 space Hausdorff space Completely Hausdorff space Regular space Tychonoff space Normal...

a totally disconnected space is a topological space that has only singletons as connected subsets. In every topological space, the singletons (and, when...

currently unknown whether the universe is simply connected like euclidean space or multiply connected like a torus. To date, no compelling evidence has...

Every hyperconnected space is both connected and locally connected (though not necessarily path-connected or locally path-connected). Note that in the definition...

unicoherent space is a topological space X {\displaystyle X} that is connected and in which the following property holds: For any closed, connected A , B ⊂...

maximal subset of a topological space that cannot be covered by the union of two disjoint non-empty open sets Connected-component labeling, an algorithm...

priori constraints) on how the space in which we live is connected or whether it wraps around on itself as a compact space. Though certain cosmological...

is the class of problems log-space reducible to the problem of determining whether two vertices in a graph are connected, which was proved to be equal...

path-connected neighbourhoods. A locally path-connected space is connected if and only if it is path-connected. Locally simply connected A space is locally...

any path-connected space Y, any two maps f,g: X → Y are homotopic. For any space Y, any map f: Y → X is null-homotopic. The cone on a space X is always...

force, through what topologists would call "a handle" of the multiply-connected space, and what physicists might perhaps be excused for more vividly terming...

a connected space, with one non-zero higher Betti number, namely, b n = 1 {\displaystyle b_{n}=1} . It does not follow that X is simply connected, only...

_{1}(S^{1})\cong \mathbb {Z} .} Any path connected, locally path connected and locally simply connected topological space X admits a universal covering. An abstract...

constructible sheaves -- a constructible sheaf on a locally path connected topological space X {\displaystyle X} is a sheaf L {\displaystyle {\mathcal {L}}}...

homotopy groups of the space. Complex projective space is compact and connected, being a quotient of a compact, connected space. From the fiber bundle...

orbit space for this action is RPn. This action is actually a covering space action giving Sn as a double cover of RPn. Since Sn is simply connected for...

a connected space such that its removal causes the resulting space to be disconnected. If removal of a point doesn't result in disconnected spaces, this...

of study in the category of uniform topological spaces Uniformly connected space – Type of uniform space "IsarMathLib.org". Retrieved 2021-10-02. Nicolas...