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...

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

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

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

existence for a certain class of base spaces. Let X {\displaystyle X} be a connected, locally simply connected topological space. Then, there exists a universal...

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...

is currently unknown whether the universe is simply connected like euclidean space or multiply connected like a torus. To date, compelling evidence has...

{\displaystyle \mathbf {v} } is defined is not a simply connected open space. Say again, in a simply connected open region, an irrotational vector field v...

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

loops. If U is simply connected, such H exists. The definition of simply connected space follows: Definition 2-2 (simply connected space). Let M ⊆ R n...

antipody quotient map from the ⁠ n {\displaystyle n} ⁠-sphere, a simply connected space. It is a double cover. The antipode map on ⁠ R p {\displaystyle...

Every simply connected space and every locally simply connected space is semilocally simply connected. (Compare with locally simply connected; here,...

_{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...

kept) Connected space Connected category Connected component (graph theory) Connected sum Cross-link Network Scale-free network Simply connected Small-world...

makes certain calculations much easier. Rational homotopy types of simply connected spaces can be identified with (isomorphism classes of) certain algebraic...

manifold which is timelike multiply connected has a diffeomorphic universal covering space which is timelike simply connected. For instance, a three-sphere...

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...

Separable space Lindelöf space Sigma-compact space Connected space Simply connected space Path connected space T0 space T1 space Hausdorff space Completely...

Let M K n {\displaystyle M_{K}^{n}} be the complete n-dimensional simply connected space of constant sectional curvature K {\displaystyle K} (and hence of...

irreducible simply connected ones (where irreducible means they cannot be written as a product of smaller symmetric spaces). The irreducible simply connected symmetric...

space is a complete, simply-connected, non-positively curved Riemannian manifold. Cartan–Hadamard theorem is the statement that a connected, simply connected...

contractible space is path connected and simply connected. Moreover, since all the higher homotopy groups vanish, every contractible space is n-connected for all...

{\displaystyle k} , let M k {\displaystyle M_{k}} denote the unique complete simply connected surface (real 2-dimensional Riemannian manifold) with constant curvature...

In topology, a branch of mathematics, a topological space X is said to be simply connected at infinity if for any compact subset C of X, there is a compact...

action by deck transformations of the fundamental group of a locally simply connected space on a universal cover is wandering and free. Such actions can be...

Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis. In geometric terms, a complete, simply connected Riemannian...

connected complete Riemannian manifold with constant curvature, but is not assumed to be simply-connected, then consider the universal covering space...

general, a space contains a 1-dimensional-boundary hole if and only if it is not simply-connected. Hence, simply-connected is equivalent to 1-connected. X is...

each space is simply connected. However, the two spaces cannot be homeomorphic because deleting a point from R2 leaves a non-simply-connected space but...

connected, or simply strong, if it contains a directed path from u to v and a directed path from v to u for every pair of vertices u, v. A connected component...