IJPAM: Volume 44, No. 4 (2008)


Joshua Campbell$^1$, David Swanson$^2$
$^{1,2}$Department of Mathematics
St. Olaf College
1520, St. Olaf Avenue, Northfield, MN 55057, USA
$^1$e-mail: campbell@stolaf.edu
$^2$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 $f$ with $f$ and $f^{-1}$ satisfying property $N$, we define an $f$-density operator and a corresponding $f$-density topology, $T_f$. In this paper, $T_f$ is proven to be a topology and general properties of the topology are developed. Classes of functions, where $T_f = T_d$ are identified and it is shown that there is a function $f$ so that $T_f \neq T_d$.

Received: March 8, 2008

AMS Subject Classification: 11B05

Key Words and Phrases: generalization of density topology, generalization of density continuous functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 4