Union of Bulgarian Mathematicians, Vol. 39, No 1, (2010), 160p-161p
Abstract:
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.
Description:
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.
