# Cross-composition product of reloids is a quasi-cartesian function

 Importance: Medium ✭✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: cross-composition product quasi-cartesian function
 Posted by: porton on: July 5th, 2012
Conjecture   Cross-composition product (for small indexed families of reloids) is a quasi-cartesian function (with injective aggregation) from the quasi-cartesian situation of reloids to the quasi-cartesian situation of pointfree funcoids over posets with least elements.

This conjecture is unsolved even for product of two multipliers.

An obviously equivalent reformulation of this conjecture for the special case of two multipliers:

Conjecture   Provided that reloids and on some set are proper filters, we can restore the values of and knowing only for every reloid on .

Reloids are defined simply as filters on a Cartesian product of two sets. The reverse reloid of a reloids is defined by the formula: . Composition of reloids and is defined as the reloid whose base is

See Algebraic General Topology for definitions of used concepts.

## Bibliography

*Victor Porton. Algebraic General Topology

* indicates original appearance(s) of problem.