Arc (topology) Created 2026-10-25 Updated 2026-11-05
View more
An arc is a space homeomorphic to , or a subset with that property. A continuous injective map from into a Hausdorff space is a homeomorphism onto its image because its domain is compact. A line segment and a semicircle are arcs; a full circle is not. A continuous path may retrace points or cross itself, so its image need not be an arc.
Read the full article