tömörségi
Tömörségi is the Hungarian term used to describe the mathematical concept of compactness. In topology, a subset K of a topological space X is compact if every open cover of K has a finite subcover; that is, from any collection of open sets whose union contains K, one can select finitely many that still cover K.
In metric spaces, compactness has several equivalent characterizations. A set is compact if and only if every
Important properties of tömörségi include:
- Continuous images of compact sets are compact.
- In Hausdorff spaces, compact sets are closed.
- A space is compact if and only if every finite intersection of closed sets with the finite
- The extreme value theorem: a continuous function defined on a compact space attains its maximum and
- Finite products of compact spaces are compact; the product of arbitrary collections is compact in general,
Common examples and non-examples help illustrate the idea. The closed interval [0,1] in R is compact, as