On (∆2) condition in density-type topologies

• Autorzy: Filipczak M. , Terepeta M.
• Języki publikacji: EN

Abstrakty

EN

We discuss properties of density-type topologies Tψ connected with condition (∆2) similar to the condition considered in the theory of Orlicz spaces. Density-type topologies Tψ introduced in [5] may not be invariant under multiplication by a number. This property is strictly connected with the condition, which we call (∆2), by analogy with well known condition introduced in Orlicz spaces. Like in the theory of Orlicz spaces, (∆2) condition causes that the considered topologies are more convenient for examination and have simpler properties. Moreover, the power functions are also of great importance as a handy instrument. Recall some basic facts. Let (Ω, Σ, μ) be a measure space and A be a family of all functions φ: [0, ∞) → [0, ∞) which are continuous, nondecreasing, such that φ(0) = 0, φ(x) > 0 for x > 0 and limx→∞ φ(x) = ∞.

Słowa kluczowe

EN

ψ-density topology; ∆2-condition; Orlicz space

PL

topologia gęstości; warunek Δ2; przestrzeń Orlicza

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 2
• Strony: 423--432
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Filipczak M.

• Department of Mathematics and Computer Science, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland

autor

Terepeta M.

• Center of Mathematics and Physics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland

Bibliografia

• [1] M. Filipczak, σ-ideals, topologies and multiplication, Bull. Soc. des Sci., Łódź 52 (2002), 11–16.
• [2] M. Filipczak, M. Terepeta, ψ-continuous functions, Rend. Circ. Mat. Palermo 58 (2009), 245–255.
• [3] J. Lukes, J. Maly, L. Zajicek, Fine Topology Methods in Real Analysis and Potential Theory, Springer, 1189, 1986.
• [4] M. M. Rao, Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, Inc., 1991.
• [5] M. Terepeta, E. Wagner-Bojakowska, ψ-density topology, Rend. Circ. Mat. Palermo 48 (2) (1999), 451–476.
• [6] E. Wagner-Bojakowska, W. Wilczyński, Comparison of ψ-density topologies, Real Anal. Exchange 25 (2) (1999/2000), 661–672.