Van der Waerden spaces and their relatives
FLAŠKOVÁ, J. Van der Waerden spaces and their relatives. Novi Sad, Srbsko, 2014.
|Anglický název:||Van der Waerden spaces and their relatives|
|Autoři:||RNDr. Jana Flašková Ph.D.|
|Abstrakt EN:||A set of natural numbers which contains arithmetic progressions of arbi- trary length is called an AP-set. According to the van der Waerden theorem sets which are not AP-sets form an ideal which is usually denoted as van der Waerden ideal. A topological space X is called van der Waerden space if for every sequence of points in X there exists a converging subsequence so that the set of indices of its elements is an AP-set, i.e. the set is positive with respect to the van der Waerden ideal. We investigate the classes of topological spaces which are defined by replacing the van der Waerden ideal in the definition of van der Waerden spaces by another suitable ideal on the natural numbers such as the summable ideal. We are interested in inclusions between such classes of spaces and we consider their topological properties (e.g. productivity). Some examples of such spaces with some additional properties are obtained as Psi-spaces for some particular almost disjoint families.|