On some properties of 𝓙-approximately continuous functions
-
Jacek Hejduk
and
Renata Wiertelak
Abstract
In this paper we will consider 𝓙-density topology connected with a sequence 𝓙 of closed intervals tending to 0 and a 𝓙-approximately continuous function associated with that kind of density points. It will be the continuation of the investigations started in “𝓙-approximately continuous functions” by J. Hejduk, A. Loranty and R. Wiertelak published in Tatra Mountains Mathematical Publications. In particular, we will show that topology generated by the sequence 𝓙 from the special family 𝔍α is always completely regular.
References
[1] Bruckner, A. M.: Differentiation of Real Functions. Lecture Notes in Math. 659, Springer-Verlag, 1978.10.1007/BFb0069821Search in Google Scholar
[2] Filipczak, T.: Density Type Topologies Generated by Functions. Traditional and present-day topics in real analysis, Łodź University Press, 2013.10.18778/7525-971-1.24Search in Google Scholar
[3] Filipczak, M.—Hejduk, J.: On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ. 28 (2004), 187–197.Search in Google Scholar
[4] Hejduk, J.—Loranty, A.—Wiertelak, R.: 𝓙-approximately continuous functions, Tatra Mt. Math. Publ. 62 (2015), 45–55.10.1515/tmmp-2015-0004Search in Google Scholar
[5] Hejduk, J.—Wiertelak, R.: On the generalization of density topologies on the real line, Math. Slovaca 64 (2014), 1267–1276.10.2478/s12175-014-0274-ySearch in Google Scholar
[6] Loranty, A.: On the generalization of the approximate continuity, Folia Math. 10 (2003), 59–65.Search in Google Scholar
[7] Wilczyński, W.: Density topologies. In: Handbook of Measure Theory, Chapter 15, (E. Pap ed.), Elsevier, 2002, pp. 675–702.10.1016/B978-044450263-6/50016-6Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Paolo de Lucia
- Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
- A note on field-valued measures
- Topologies and uniformities on d0-algebras
- On some properties of 𝓙-approximately continuous functions
- Porous subsets in the space of functions having the Baire property
- Rademacher’s theorem in Banach spaces without RNP
- Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
- Measure games on pseudo-D-lattices
- On some properties of k-subadditive lattice group-valued capacities
- Lp Spaces in vector lattices and applications
- The Choquet integral with respect to fuzzy measures and applications
- A note on the range of vector measures
- Ideal convergent subsequences and rearrangements for divergent sequences of functions
- Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
- A generalization of the exponential sampling series and its approximation properties
- Monotonicity and total boundedness in spaces of “measurable” functions
- Vector lattices in synaptic algebras
- Density, ψ-density and continuity
- Feather topologies
- On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
- Rate of convergence of empirical measures for exchangeable sequences
- On non-additive probability measures
- Equi-topological entropy curves for skew tent maps in the square
- On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
