locally arcwise connected topological space

locally arcwise connected topological space

[′lō·kə·lē ′ärk‚wīz kə‚nek·təd ¦täp·ə¦läj·ə·kəl ¦spās] (mathematics) A topological space in which every point has an arcwise connected neighborhood, that is, an open set any two points of which can be joined by an arc.