# A diagram about funcoids and reloids

Define for posets with order :

- ;
- .

Note that the above is a generalization of monotone Galois connections (with and replaced with suprema and infima).

Then we have the following diagram:

What is at the node "other" in the diagram is unknown.

**Conjecture**"Other" is .

**Question**What repeated applying of and to "other" leads to? Particularly, does repeated applying and/or to the node "other" lead to finite or infinite sets?

See Algebraic General Topology for definitions of used concepts.

The known part of the diagram is considered in this file.

## Bibliography

* indicates original appearance(s) of problem.

### The diagram was with an error

On November 26th, 2016 porton says:

My diagram was with an error. I have uploaded a corrected version of the diagram.

--

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

## The value of node "other"

It seems that the node "other" is not .

I conjecture where is the reloid defined by the cofinite filter on and thus for all singletons and for every nontrivial atomic filter .

This is my very recent thoughts and yet needs to be checked.

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