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locally arcwise connected topological space

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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.

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