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...

a connected (resp. locally connected, path-connected, locally path-connected) space is connected (resp. locally connected, path-connected, locally path-connected)...

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

but not locally contractible (if it were, it would be locally connected which it is not). Locally contractible spaces are locally n-connected for all...

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

of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize...

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...

of connectedness. The comb space, C, is path connected and contractible, but not locally contractible, locally path connected, or locally connected. The...

is connected). Locally Riemannian symmetric spaces that are not Riemannian symmetric may be constructed as quotients of Riemannian symmetric spaces by...

theorem states that, for locally connected spaces, unicoherence is equivalent to a separation property of the closed sets of the space. Charatonik, Janusz...

locally constant. The converse will hold if its domain is a connected space. Every locally constant function from the real numbers R {\displaystyle \mathbb...

topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications...

(2001) [1994], "Poincaré space", Encyclopedia of Mathematics, EMS Press Edward G. Begle (1942). "Locally Connected Spaces and Generalized Manifolds"...

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

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

projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself. In particular, coverings...

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

itself. Locally connected. A space is locally connected if every point has a local base consisting of connected sets. Totally disconnected. A space is totally...

continuous with exponent α, where 0 < α ≤ 1. This is a locally convex topological vector space. If the Hölder coefficient | f | C 0 , α = sup x , y ∈...

{\displaystyle \{C_{j}\}} is the collection of components of a locally connected space X {\displaystyle X} , there is a natural isomorphism H ¯ q ( X...

reciprocity See Weil reciprocity. Zariski–Riemann space A Zariski–Riemann space is a locally ringed space whose points are valuation rings. Proof: Let D...

Euclidean space at large distances, and to have a self-dual Riemann tensor. Mathematically, this means that they are asymptotically locally Euclidean...

topological vector space is locally convex if and only if its topology is induced by a family of seminorms. Let X {\displaystyle X} be a vector space over either...

locally compact can arise as a result of the different choices of these conditions. Locally compact topological spaces Locally connected and Locally path-connected...

Hausdorff or locally connected. A space in which all components are one-point sets is called totally disconnected. Related to this property, a space X is called...

locally convex. Other well-known examples of TVSs include Banach spaces, Hilbert spaces and Sobolev spaces. Many topological vector spaces are spaces...

a point. As topological spaces, all the ordinals are Hausdorff and even normal. They are also totally disconnected (connected components are points),...

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

it is both R0 and T0. A finite T1 space is necessarily discrete (since every set is closed). A space that is locally T1, in the sense that each point has...

In mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all distinct pairs of elements of the set in...