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 $I_nP$-$n$-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 $\bigcup_{k=1}^n\Delta_{\varphi}\omega(K^{k-1},G\setminus B_{\mu},K^{n-k})\ne G$ for all $\mu\in M$ and every finite subsets $K$ of $G$. In particular, we continue the line of research from [6, 9].