Diagonalizations of dense families

Abstract

Abstract. We develop a unified framework for the study of classic and new properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods and constructions scattered in the literature, and on some novel results concerning the classic properties.

Selective versions of chain condition-type properties

“…While other selective properties have been characterized on P R(X) (see, for example, [11] and [8]), the problem of characterizing the selective ccc of P R(X) has remained open. We introduce a new selection principle to provide such a characterization and then reduce the selective ccc of the Pixley-Roy hyperspace of a separable metrizable space X to a well-known selective covering property of X.…”

Some weak covering properties and infinite games

“…The property S 1 (D o D o ) is studied furthermore in Aurichi [3] under the name selective CCC. Also in [5], the readers can see an extensive summary on selection principles concerning dense subspaces.…”

Variations of selective separability and tightness in function spaces with set-open topologies

“…It should be noted that very recently Tsaban and his co-authors in [6] The selection principle theory is firstly considered in bitopological spaces by Kočinac andÖzçag in [14,15] and they carried out a systematic study on selection principles mainly selective versions of separability in bitopological spaces, particularly in the space C(X) of all continuous real-valued functions defined on a Tychonoff space X, where C(X) is endowed with the topology τ p of pointwise topology and the compact-open topology τ k .…”