Resolvability of some special algebras with topologies

Liubomir Chiriac

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 92-105.

Résumé

Let $G$ be an infinite $I_{n}P$-$n$-groupoid. We construct a disjoint family $\{B_{\mu }:\mu \in M\}$ of non-empty subsets of $G$ such that the sets $\{B_{\mu }\}$ are dense in all Choban's totally bounded topologies on $G$, $|M|=|G|$, $G=\bigcup \{B_{\mu }:\mu \in M\}$ and $\bigcup _{k=1}^n{\mathrm{\Delta }}_{\phi }\omega (K^{k-1},G\setminus B_{\mu },K^{n-k})\ne G$ for all $\mu \in M$ and every finite subsets $K$ of $G$. In particular, we continue the line of research from [6, 9].

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