# A diagram about funcoids and reloids

 Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: Galois connections
 Posted by: porton on: November 26th, 2016

Define for posets with order :

1. ;
2. .

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

Blog post

* indicates original appearance(s) of problem.

### 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

### The diagram was with an error

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

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