Abstract
In this paper will be considered density-like points and density-like topology in the family of Lebesgue measurable subsets of real numbers connected with a sequence đ= {Jn}nââ of closed intervals tending to zero. The main result concerns necessary and sufficient condition for inclusion between that defined topologies.
References
[1] Ciesielski, K.âLarson, L.âOstaszewski, K.: đ-density continuous functions, Mem. Amer. Math. Soc. 107(515) (1994).10.1090/memo/0515Search in Google Scholar
[2] Filipczak, M.âFilipczak, T.âHejduk, J.: On the comparison of the density type topologies, Atti Sem. Mat. Fis. Univ. Modena LII (2004), 1â11.Search in Google Scholar
[3] Filipczak, M.âHejduk, J.; On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ. 28 (2004), 187â197.Search in Google Scholar
[4] Hejduk, J.âLoranty, A.âWiertelak, R.: On đ-continuous functions, Tatra Mt. Math. Publ., to appear.10.1515/tmmp-2016-0004Search in Google Scholar
[5] Hejduk, J.âWiertelak, R.: On the generalization of density topologies on the real line, Math. Slovaca 64 (2014), 1267â1276.10.2478/s12175-014-0274-ySearch in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- On the number of cycles in a graph
- Characterization of posets for order-convergence being topological
- Classification of posets using zero-divisor graphs
- On a generalized concept of order relations on B(H)
- A study of stabilizers in triangle algebras
- Revealing two cubic non-residues in a quadratic field locally
- Codensity and stone spaces
- Big mapping class groups are not acylindrically hyperbolic
- Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations
- Starlike and convex functions with respect to symmetric conjugate points involving conical domain
- Summations of Schlömilch series containing anger function terms
- Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals
- Nuclear operators on Cb(X, E) and the strict topology
- More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
- Matrix generalized (Ξ, Ï)-derivations on matrix Banach algebras
- Nonlinear â-Jordan triple derivations on von Neumann algebras
- Addendum to âA sequential implicit function theorem for the chords iterationâ, Math. Slovaca 63(5) (2013), 1085â1100
- Comparison of density topologies on the real line
- Rational homotopy of maps between certain complex Grassmann manifolds
- Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields
- Rotheâs method for physiologically structured models with diffusion
- Zero-divisor graphs of lower dismantlable lattices II
- An identity of symmetry for the degenerate Frobenius-Euler Polynomials
Articles in the same Issue
- On the number of cycles in a graph
- Characterization of posets for order-convergence being topological
- Classification of posets using zero-divisor graphs
- On a generalized concept of order relations on B(H)
- A study of stabilizers in triangle algebras
- Revealing two cubic non-residues in a quadratic field locally
- Codensity and stone spaces
- Big mapping class groups are not acylindrically hyperbolic
- Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations
- Starlike and convex functions with respect to symmetric conjugate points involving conical domain
- Summations of Schlömilch series containing anger function terms
- Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals
- Nuclear operators on Cb(X, E) and the strict topology
- More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism
- Matrix generalized (Ξ, Ï)-derivations on matrix Banach algebras
- Nonlinear â-Jordan triple derivations on von Neumann algebras
- Addendum to âA sequential implicit function theorem for the chords iterationâ, Math. Slovaca 63(5) (2013), 1085â1100
- Comparison of density topologies on the real line
- Rational homotopy of maps between certain complex Grassmann manifolds
- Examples of random fields that can be represented as space-domain scaled stationary Ornstein-Uhlenbeck fields
- Rotheâs method for physiologically structured models with diffusion
- Zero-divisor graphs of lower dismantlable lattices II
- An identity of symmetry for the degenerate Frobenius-Euler Polynomials