I’ve added the following to my research book:
Galois surjection is the special case of Galois connection such that is identity.
For Galois surjection such that is a join-semilattice we have (for every )
(Don’t confuse this my little theorem with the well-known theorem with similar formula formula .)
This formula in particular applies to the Galois connection between funcoids and reloids (see my book).
After noticing an error in my math book, I rewritten its section “Funcoids and filters” to reflect that .
Previously I proved an example demonstrating that , but this example is believed by me to be wrong. The example was removed from the book.
Thus I removed all references to (as it is the same as ) and reworked the chapter “Funcoids and filters” to reflect the change.
The book is available free of change at this Web page.
The story of the past:
was defined by the formula .
From the theorem in “The diagram” section (the theorem with a diagram) it trivially follows that . It follows trivially, but I have found this only today.