Geodesic
Compacta are maximally $G_\delta$-resolvable
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 259-261

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It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum $X$ contains $\Delta(X)$ many pairwise disjoint dense subsets, where $\Delta(X)$ denotes the minimum size of a non-empty open set in $X$. The aim of this note is to prove the following analogous result: Every compactum $X$ contains $\Delta_\delta(X)$ many pairwise disjoint $G_\delta$-dense subsets, where $\Delta_\delta(X)$ denotes the minimum size of a non-empty $G_\delta$ set in $X$.
Classification : 03E10, 54A25, 54D30
Keywords: compact spaces; $G_\delta $-sets; resolvability 
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Juhász, István; Szentmiklóssy, Zoltán. Compacta are maximally $G_\delta$-resolvable. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 259-261. http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a10/