Compositions of porouscontinuous functions
-
Stanisław Kowalczyk
and
Małgorzata Turowska
Abstract
The notion of porouscontinuity was introduced by Borsík and Holos. We find classes of functions whose compositions with porouscontinuous functions are still porouscontinuous. Next, we study compositions of porouscontinuous functions with homeomorphisms. We investigate connections between 𝓘𝓒(𝓐) ∩ 𝓗𝓞𝓜 and 𝓘𝓒(𝓑) ∩ 𝓗𝓞𝓜 for different classes 𝓐,𝓑 ∈ 𝓟𝓒, where 𝓟𝓒 is the set of all classes of porouscontinuous functions and 𝓗𝓞𝓜 is the set of all homeomorphisms f : ℝ → ℝ.
Communicated by Ján Borsík
References
[1] Borsík, J.—Holos, J.: Some properties of porouscontinuous functions, Math. Slovaca 64(3) (2014), 741–750.10.2478/s12175-014-0237-3Search in Google Scholar
[2] Bruckner, A. M.: Differentation of Real Functions. Lecture Notes in Math. 659, Springer-Verlag, 1978.10.1007/BFb0069821Search in Google Scholar
[3] Kowalczyk, S.—Nowakowska, K.: Maximal classes for ϱ-upper continuous functions, J. Appl. Anal. 19 (2013), 69–89.10.1515/jaa-2013-0005Search in Google Scholar
[4] Kowalczyk, S.—Turowska, M.: On structural properties of porouscontinuous functions, Math. Slovaca 67(5) (2017), 1239–1250.10.1515/ms-2017-0045Search in Google Scholar
[5] Kowalczyk, S.: Compositions of ϱ-upper continuous functions, Math. Slovaca 66(3) (2016), 1–16.10.1515/ms-2015-0162Search in Google Scholar
[6] Ostaszewski, K.: Continuity in the Density Topology, Real Anal. Exchange 7 (1981/82), 259–269.10.2307/44153412Search in Google Scholar
[7] Zajíček, L.: Porosity and σ-porosity, Real Anal. Exchange 13 (1987/88), 314–350.10.2307/44151885Search in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Prof. RNDr. pavel brunovský, DrSc. passed away ∗dec. 5, 1934 – † dec. 14, 2018
- Ideals and congruences in pseudo-BCH algebras
- Regular double p-algebras
- Distributive nearlattices with a necessity modal operator
- States in generalized probabilistic models: An approach based in algebraic geometry
- Free power-associative n-ary groupoids
- On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
- On the space of generalized theta-series for certain quadratic forms in any number of variables
- Uniqueness and periodicity for meromorphic functions with partial sharing values
- Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
- An inverse boundary problem for fourth-order Schrödinger equations with partial data
- Entropy as an integral operator
- Global behavior of two third order rational difference equations with quadratic terms
- Measures on effect algebras
- Some topological and combinatorial properties preserved by inverse limits
- The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
- Compositions of porouscontinuous functions
- A note on prime divisors of polynomials P(Tk); k ≥ 1
- On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications
- Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations
