Generalized path-connectedness in proximity spaces ★★
Author(s): Porton
Let be a proximity.
A set is connected regarding iff .
Conjecture The following statements are equivalent for every endofuncoid and a set :
- \item is connected regarding . \item For every there exists a totally ordered set such that , , and for every partion of into two sets , such that , we have .
Keywords: connected; connectedness; proximity space
Dirac's Conjecture ★★
Author(s): Dirac
Conjecture For every set of points in the plane, not all collinear, there is a point in contained in at least lines determined by , for some constant .
Keywords: point set