arcwise disconnected

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Connected space — For other uses, see Connection (disambiguation). Connected and disconnected subspaces of R² The green space A at top is simply connected whereas the blue space B below is not connected … Wikipedia
Continuum (topology) — In the mathematical field of point set topology, a continuum (pl continua) is a nonempty compact connected metric space, or less frequently, a compact connected Hausdorff topological space. Continuum theory is the branch of topology devoted to… … Wikipedia

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