## 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