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On Lower and Semi-Lower Density Operators
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Jacek Hejduk
Published/Copyright:
March 10, 2010
Abstract
This paper contains some results connected with topologies generated by lower and semi-lower density operators. We show that in some measurable spaces (𝑋, 𝑆, 𝐽) there exists a semi-lower density operator which does not generate a topology. We investigate some properties of nowhere dense sets, meager sets and σ-algebras of sets having the Baire property, associated with the topology generated by a semi-lower density operator.
Key words and phrases:: Lower density operator; density topology; topology generated by lower density operator; sets having the Baire property
Received: 2006-05-31
Revised: 2007-01-22
Published Online: 2010-03-10
Published in Print: 2007-December
© Heldermann Verlag
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Keywords for this article
Lower density operator;
density topology;
topology generated by lower density operator;
sets having the Baire property
Articles in the same Issue
- On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations
- On Wiener's Criterion for an Elliptic Equation with Nonuniform Degeneration
- A Modified Quasi-Reversibility Method for a Class of Ill-Posed Cauchy Problems
- Convergence of Walsh–Fourier Series of a Class 𝐵𝑂(𝑝(𝑛) ↑ ∞)
- Rate of Convergence for the Bézier Variant of the MKZD Operators
- On Lower and Semi-Lower Density Operators
- Szegö Asymptotics of Extremal Polynomials on the Segment [–1, +1]: The Case of a Measure with Finite Discrete Part
- Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane
- Vector Measures on Topological Spaces
- Positive Solutions for Neutral Difference Equations with Continuous Arguments
- Elusive Examples of Non-Metrizable Continua which Admit a Whitney Map
- Rate of Convergence in Recursive Parameter Estimation Procedures
- Oscillation Theorems for Differential Equations Involving Even Order Nonlinear Sturm–Liouville Operator
- On the Absolute Convergence of Fourier Series of Functions of ∧𝐵𝑉(𝑝) and φ ∧𝐵𝑉
- Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems
- Stability of Finite Difference Schemes on Irregular Meshes for Von Foerster-Type 1-D Equations
- Corrigenda to “On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces”
