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...

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...

guarantee its existence: Let X {\displaystyle X} be a connected, locally simply connected topological space; then, there exists a universal covering p : X ~...

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

consistent with the universe having infinite extent and being a simply connected space, though cosmological horizons limit our ability to distinguish between...

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

{\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...

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...

_{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...

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

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

metric space is a metric space where any two points are the endpoints of a minimizing geodesic. Hadamard space is a complete simply connected space with...

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...

kept) connected space connected category connected component (graph theory) connected sum cross-link network Scale-free network simply connected small-world...

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

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

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...

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...

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...

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

into a point without exiting the space.) The first version is a special case of this because on a simply connected set, every closed curve is homotopic...

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

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...

{\displaystyle k} . Simply connected spaces and simple spaces are (trivial) examples of nilpotent spaces; other examples are connected loop spaces. The homotopy...

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

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...

n-space, the n-dimensional sphere, and hyperbolic space, although a space form need not be simply connected. The Killing–Hopf theorem of Riemannian geometry...