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...

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...

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...

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...

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

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...

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...

{\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...

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

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

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...

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...

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

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

_{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...

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...

}}} . Let p′q′r′ be a geodesic triangle in the model space Mδ, i.e. the simply connected space of constant curvature δ, such that the lengths of sides...

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...

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

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...

the corollary of the aforementioned result, that for a pointed, simply connected space X, the following isomorphism holds: U ( π ∗ ( Ω X ) ⊗ Q ) ≅ H ∗...

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

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

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...

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

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