$\mathsf{SOCA}$ and $\mathsf{OGA}$ for $\mathsf{HL}$ spaces with strong properties

Autor:	Corona-García, José Antonio, Ongay-Valverde, Iván, Ramos-García, Ulises Ariet
Rok vydání:	2022
Předmět:	Mathematics - General Topology Mathematics - Logic Primary 54D20 03E65 Secondary 54A35 03E15
Druh dokumentu:	Working Paper
Popis:	We study open colorings in certain classes of hereditary Lindel\"{o}f ($\mathsf{HL}$) spaces and submetrizable spaces. In particular, we show that the definible version for the Open Graph Axiom ($\mathsf{OGA}$) holds for the class of $\mathsf{HL}$ strong Choquet submetrizable spaces extending a well-known result of Feng. Furthermore, we show the consistency of the Open Graph Axiom for regular spaces that have countable spread and it's square also has it, reaching closer to a well known conjecture of Todor\v{c}evi\'{c}: "It is consistent that all regular spaces with countable spread satisfy $\mathsf{OGA}$". Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.06650 Zobrazit plný text záznamu View this record from Arxiv