## New theorem about relationships between funcoids and reloids

I have proved (the proof is currently available in this file) that are components of a pointfree funcoid between boolean

A new (but easy to prove) theorem in my research book: Theorem Let and be endomorphisms of some partially ordered

## \$T_4\$-funcoids

I have added to my free ebook a definition of -funcoids (generalizing topologies). A funcoid is iff . This can

## A new easy theorem about pointfree funcoids

I have added the following easy to prove theorem to my general topology research book: Theorem If and are bounded

## A new math abstraction, categories of sides

I introduce a new math abstraction, categories of sides, in order to generalize two theorems into one. Category of sides

## A new negative result in pointfree topology

I have proved the following negative result: Theorem is not boolean if is a non-atomic boolean lattice. The theorem is

## Galois connections are related with pointfree funcoids!

I call pointfree funcoids (see my free e-book) between boolean lattices as boolean funcoids. I have proved that: Theorem Let

## I’ve partially proved a conjecture

The following is a conjecture: Conjecture The set of pointfree funcoids between two boolean lattices is itself a boolean lattice.