On supratopologies, normalized families and Frankl conjecture

Autor: Carvalho, André, Machiavelo, António
Rok vydání: 2024
Předmět:
Druh dokumentu: Working Paper
Popis: We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl conjecture to some families of so-called supratopological spaces. We prove some results on the structure of normalized families, presenting a new way of reducing such a family to a smaller one using dual families. Applying our reduction method, we prove a refinement of a conjecture originally proposed by Poonen. Finally, we show that Frankl Conjecture holds for the class of families obtained from successively applying the reduction process to a power set.
Comment: 27 pages, 1 figure. comments are welcome!
Databáze: arXiv