Jordan, n.3
Etymology: Name of Marie Ennemond Camille Jordan (1838–1922), French mathematician.
Math.
Jordan curve, any curve that is topologically equivalent to a circle, i.e. is closed and does not cross itself; so Jordan('s) (curve) theorem , the theorem that any Jordan curve in a plane divides the plane into just two distinct regions having the curve as their common boundary.
1900 W. F. Osgood in Trans. Amer. Math. Soc. 1 310
By a Jordan curve is meant a curve of the general class of continuous curves without multiple points, considered by Jordan, Cours d'Analyse, vol. I, 2d edition, 1893, p. 90.
1919 Ann. Math. XXI. 180
(heading)
A proof of Jordan's theorem about a simple closed curve.
1939 M. H. A. Newman Elem. Topol. Plane Sets of Points vi. 132
Theorem 2·3. (Jordan's Theorem for a polygon.) A simple polygon determines two domains, of each of which it is the frontier.
1947 R. Courant & H. E. Robbins What is Math.?
(ed. 4)
v. 246
The Jordan curve theorem is quite simple to prove for the reasonably well-behaved curves, such as polygons or curves with continuously turning tangents, which occur in most important problems.
1965 S. Barr Exper. Topol. i. 13
A Jordan curve can be drawn on the side of the torus and still divide it into two, but not if it circles, or goes through the hole.
1900—1965(Hide quotations)