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A locally path connected space [3] [1] is a space that is locally path connected at each of its points. Locally path connected spaces are locally connected. The converse does not hold (see the lexicographic order topology on the unit square ).
Every locally path-connected space is locally connected. A locally path-connected space is path-connected if and only if it is connected. The closure of a connected subset is connected. Furthermore, any subset between a connected subset and its closure is connected. The connected components are always closed (but in general not open) The ...
In mathematics, specifically algebraic topology, 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 semi-locally simply connected if there is a lower bound on the sizes of the “holes” in X .
A space is locally path-connected if every point has a local base consisting of path-connected sets. A locally path-connected space is connected if and only if it is path-connected. Arc-connected. A space X is arc-connected if for every two points x, y in X, there is an arc f from x to y, i.e., an injective continuous map : [,] with () = and ...
A space is locally path-connected if every point has a local base consisting of path-connected neighbourhoods. [15] A 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 has a local base consisting of simply connected neighbourhoods. Loop
In mathematics, a locally simply connected space is a topological space that admits a basis of simply connected sets. [1] [2] Every locally simply connected space is also locally path-connected and locally connected. The Hawaiian earring is not locally simply connected. The circle is an example of a locally simply connected space which is not ...
The space is homeomorphic to the one-point compactification of the union of a countable family of disjoint open intervals. The Hawaiian earring is a one-dimensional, compact, locally path-connected metrizable space.
Local systems have a mild generalization to constructible sheaves-- a constructible sheaf on a locally path connected topological space is a sheaf such that there exists a stratification of X = ∐ X λ {\displaystyle X=\coprod X_{\lambda }}