On supratopologies, normalized families and Frankl conjecture
Autor: | Carvalho, André, Machiavelo, António |
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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 |
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