# Generalized path-connectedness in proximity spaces

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.

## A proposed lemma

http://math.stackexchange.com/questions/691643/a-lemma-to-solve-a-conjec...

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Victor Porton - http://www.mathematics21.org