Convergence in van der Waerden and Hindman spaces (Q471493)

Using the notions of convergence with respect to an ideal, four classes of topological spaces are defined, two of them being subclasses of the sequentially compact spaces and the other two being subclasses of the countably compact spaces. Some properties of them are analyzed and studied, finally the authors choose two particular ideals connected with well known theorems, namely the van der Waerden theorem and the Hindman theorem, in order to obtain that the two classes of the considered spaces agree with the van der Waerden ideal and the Hindman ideal respectively