# IJPAM: Volume 44, No. 4 (2008)

FAMILIES OF DENSITY TYPE TOPOLOGIES

Joshua Campbell, David Swanson
Department of Mathematics
St. Olaf College
1520, St. Olaf Avenue, Northfield, MN 55057, USA
e-mail: campbell@stolaf.edu
e-mail: swansondav@gmail.com

Abstract.Originally defined by Haupt and Pauc in 1952, the density topology has since been well-studied. Consequently a Baire category analogue of the density topology was developed by Ciesielski and Larson (1993) and Wilczynski (1984). This paper presents another variation on the density topology. Given an arbitrary homeomorphism with and satisfying property , we define an -density operator and a corresponding -density topology, . In this paper, is proven to be a topology and general properties of the topology are developed. Classes of functions, where are identified and it is shown that there is a function so that .