Geodesic
Every N-Dimensional Separable Metric Space Contains a Totally Disconnected (n-1)-Dimensional Subset with no True Quasi-Components
Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 160-161.

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The quasi-component Q(x) of a point x of a topological space X is by definition the intersection of all open and closed subsets of X, every one of which contains x. If a quasi-component consists of more than one point, it is called a true quasi-component. In this note we give a simple construction of (at least) (n − 1)-dimensional totally disconnected subspace Y of a given n-dimensional separable metric space X such that every quasi-component in Y is a single point. *2000 Mathematics Subject Classification: 17C55.
Keywords: Totally Disconnected N-Dimensional Space 
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Todorov, Vladimir; Stoev, Petar. Every N-Dimensional Separable Metric Space Contains a Totally Disconnected (n-1)-Dimensional Subset with no True Quasi-Components. Mathematics and Education in Mathematics, Tome 39 (2010) no. 1, pp. 160-161. http://geodesic.mathdoc.fr/item/MEM_2010_39_1_a14/