# Generalized path-connectedness in proximity spaces

 Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: connected connectedness proximity space
 Posted by: porton on: February 1st, 2014

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 .

## Bibliography

*Question at math.StackExchange.com by Victor Porton

* indicates original appearance(s) of problem.