Wagner-Bojakowska, Elżbieta; Wilczyński, Władysław Comparison of \(\psi\)-density topologies. (English) Zbl 1016.26001 Real Anal. Exch. 25(1999-2000), No. 2, 661-672 (2000). Summary: The paper includes a necessary and sufficient condition under which two \(\psi\)-density topologies generated by two functions \(\psi_1\) and \(\psi_2\) are equal. The condition is formulated in terms of the behavior of two sequences of sets \[ A^+_k= \{x\in \mathbb{R}_+: \psi_1(2x)<\textstyle{{1\over k}}\psi_2(2x)\} \] and \[ B^+_k= \{x\in \mathbb{R}_+: \psi_2(2x)< \textstyle{{1\over k}}\psi_1(2x)\}. \] {}. Cited in 3 Documents MSC: 26A03 Foundations: limits and generalizations, elementary topology of the line 28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable Keywords:density topology; approximate continuity; change of topology; comparison of topologies PDFBibTeX XMLCite \textit{E. Wagner-Bojakowska} and \textit{W. Wilczyński}, Real Anal. Exch. 25, No. 2, 661--672 (2000; Zbl 1016.26001)