Every N-Dimensional Separable Metric Space Contains a Totally Disconnected (n-1)-Dimensional Subset with no True Quasi-Components

Владимир Тодоров, Петър Стоев - Тази бележка съдържа елементарна конструкция на множество с указаните в заглавието свойства. Да отбележим в допълнение, че така полученото множество остава напълно несвързано дори и след като се допълни с краен брой елементи.

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.