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1
Content available Nieoczywistości ciągłości
Gawron Piotr
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2023
|
Nr 5
256-260
PL
Przytaczamy definicje ciągłości funkcji rzeczywistej i nieoczywiste przykłady jej zastosowania.
2
Content available Uwagi o ewolucji pojęcia ciągłości
Gawron Piotr
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2021
|
Nr 3
255-257
PL
Pojęcie funkcji ciągłej a ogólniej ciągłości leży u podstaw analizy matematycznej. W tym artykule przestawimy krótko kilka uwag natury historycznej o ewolucji definicji ciągłości funkcji. Czytelników bardziej zainteresowanych tym zagadnieniem zachęcamy do zapoznania się z załączoną literaturą a w szczególności pozycjami [2], [4], [7], [12] mimo, że nie we wszystkich pracach autorzy mają podobne poglądy.
3
Content available remote Topological Characterisation of Multi-Buffer Simulation
Hutagalung Milka
Fundamenta Informaticae
|
2021
|
Vol. 178, nr 1/2
77--99
EN
Multi-buffer simulation is an extension of simulation preorder that can be used to approximate inclusion of languages recognised by Büchi automata up to their trace closures. DUPLICATOR can use some bounded or unbounded buffers to simulate SPOILER ’s move. It has been shown that multi-buffer simulation can be characterised with the existence of a continuous function. In this paper, we show that such a characterisation can be refined to a more restricted case, that is, to the one where DUPLICATOR only uses bounded buffers, by requiring the function to be Lipschitz continuous instead of only continuous. This characterisation however only holds for some restricted classes of automata. One of the automata should only produce words where each letter cannot commute unboundedly. We show that this property can be syntactically characterised with cyclic-path-connectedness, a refinement of syntactic condition on automata that have regular trace closure. We further show that checking cyclic-path-connectedness is indeed co-NP-complete.
4
Content available On monotonicity of real functions
Jędrzejewski J. M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2017
|
Vol. 22
49--60
EN
Monotonicity of functions were of great interest of many mathematicians. Starting from the well known theorem of monotonicity of a differentiable function one can get quite sophisticated results. We give a survey of results when thesis of them is continuous and monotone function. Someone can ask why it should be continuous. Even a differentiable functions but not at the only point of its domain with positive derivative need not be non-decreasing. That is why we want to look for theorems for continuous functions.
5
Content available A note on weakly ϱ-upper continuous functions
Nowakowska K., Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
195--206
EN
In the article we present definition and some properties of weakly ϱ-upper continuous functions. We find maximal additive and maximal multiplicative families for the class of weakly ϱ-upper continuous functions.
6
Content available On the almost uniform convergence
Drozdowski R., Jędrzejewski J., Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2013
|
Vol. 18
11--17
EN
Uniform convergence for continuous real functions sequences preserves continuity of the limit of such sequences. There are weaker types of convergence which have similar properties. We consider such types of convergence for functions from one topological space into another one.
7
Maximal classes for rho-upper continuous functions
Kowalczyk S., Nowakowska K.
Journal of Applied Analysis
|
2013
|
Vol. 19, nr 1
69--89
EN
In this paper we present some properties of ρ-upper continuous functions. We give a condition equivalent to ρ-upper continuity and find maximal additive and maximal multiplicative classes for the family of ρ-upper continuous functions. These classes depend on whether ρ<1 or ρ=1. To describe maximal additive and maximal multiplicative classes for 1-upper continuous function, we need the notions of sparsity and T*topology.
8
Content available Some algebraic properties of preponderantly continuous functions
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
Vol. 16
39--46
EN
In the presented paper we study some properties of preponderantly continuous functions and functions satisfying the property A1. For any family F of real-valued functions we define MAXF = {g: max{f,g} ∈ F for all f ∈ F} and MINF = {g: min{f,g} ∈ F for all f ∈ F}. The aim of the paper is to find MINF for two discussed classes of functions.
9
Content available Comparison of ψ -sparse topologies
Goździewicz-Smejda A., Łazarow E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
Vol. 14
21-36
EN
The paper includes a necessary condition and sufficient conditions under which two ψ -sparse topologies generated by two functions ψ1 and ψ 2 are equal. Additionally we proved that the intersection of all ψ -sparse topologies is equal to the Hashimoto topology.
10
Content available remote Perfectly continuous functions
Kohli J., Singh D.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 1
221-231
EN
A new class of functions called [...]perfectly continuous functions is introduced and their basic properties are studied. Their place in the hierarchy of other variants of continuity that already exist in the literature is elaborated. Further, it is shown that if X is sum connected (e.g. connected or locally connected) and Y is Hausdorff, then the function space PA (X, Y] of all (...]-perfectly continuous functions from X into Y is closed in Yx in the topology of pointwise convergence.
11
Content available remote Maximal classes for the family of quasi-continuous functions with closed graph
Sieg W.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 1
41-45
EN
In this paper we consider classes of functions f : R - R. The maximal additive class for the family QU of quasi-continuous functions with closed graph is equal to the class of all continuous functions. We also show that the maximal multiplicative class for QU is equal to a class of continuous functions, which fulfil an extra condition.
12
Content available remote On some forms of weakly continuous functions in bitopological spaces
Noiri T., Popa V.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 3
685-700
EN
As a generalization of weakly continuous functions, we introduce the notion of (i, j)-weakly m-continuous functions in bitopological spaces and obtain unified characterizations and properties of certain forms of weakly continuous functions in bitopological spaces.
13
Content available remote Baire measurability of (M,N)-Wright convex functions
Lewicki M.
Commentationes Mathematicae
|
2008
|
Vol. 48, [Z] 1
75-83
EN
Let I ⊆R be an open interval and M,N : I^2 →1be means on I. Let [formula] We give sufficient conditions on M,N and the function &fi;such that for every Baire measurable solution R of the functional inequality [formula].
14
Content available remote On an extension for functions
Ekici E.
Demonstratio Mathematica
|
2006
|
Vol. 39, nr 3
657-670
EN
A new classes of functions, called strongly na-precontinuous functions, strongly na-continuous functions and na-continuous functions have been introduced. This paper considers the class of sigmas -na-continuous functions and its relationships to semi-regularization topologies, the other related functions. Preservation of appropriate topo-logical properties by sigmas -na-continuous functions is investigated.
15
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
Noiri T., Popa V.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 1
223--234
EN
In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
16
Content available remote On the recursive sequence Xn+1=alfa+Xn-k:f(Xn,....Xn-k+1)
Karakostas G., Stevic S.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 3
595-610
EN
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form Xn+l=alfa+Xn-k:f(Xn,....Xn-k+1, n=0, 1, ..... is investigated, where alfa > 0, k is an element of N and f : [0,infinity)- (0,infinity)k is a continuous function nondecreasing in each variable.
17
Content available remote On the notion of (gamma, s)-continuous functions
Ekici E.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 3
715--727
EN
In 2002, Noiri and Jafari studied the notion of (0, s-continuous functions due to Thompson [Proc. Amer. Math. Soc. 60 (1976) 335-338]. In this paper, a new generalization of (0, s-continuity which is called (gamma, s)-continuity is introduced and studied. Furthermore, characterizations, basic properties, preservation theorems of (gamma,s)- continuous functions and relationships between (gamma, s)-continuous functions and the other types of functions are investigated and obtained.
18
Content available remote On the maxima of two functions which are simultaneously unilaterally approximately continuous and approximately regulated
Grande M.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 3
523--531
EN
In this article we investigate the maxima of two unilaterally approximately continuous and approximately regulated functions. In particular we prove that if / is the maximum of two unilaterally approximately continuous and approximately regulated functions then for each x is an element of Dunap(f) = {x : f is not unilaterally approximately continuous at x} the inequality f(x) < max(fap(x+),fap(x-)) holds. Moreover, we show some condition ensuring that an approximately regulated function f such that Dap(f) is countable and for each x is an element of Dunap(f) the inequality f(x) < max(fap(x+),fap(x-)) holds, is the maximum of two unilaterally approximately continuous and approximately regulated functions.
19
Content available remote Characterization of continuous functions by class C(infinity) curves
Najdecki A., Tabor J.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 1
31--34
EN
Let f : X -Y, where X is a Banach space and Y is a Hausdorff topological space. We prove that if f o (gamma) is continuous for every curve (gamma) : [0,1] -> X of class C(infinity), then f is continuous.
20
Content available remote On a weak form of almost weakly continuous functions
Baker C.
Demonstratio Mathematica
|
2000
|
Vol. 33, nr 4
865-872
EN
A weak form of almost weak continuity, called subalmost weak continuity, is introduced. It is shown that subalmost weak continuity is strictly weaker than both almost weak continuity and subweak continuity. Subalmost weak continuity is used to improve a result in the literature concerning the graph of an almost weakly continuous function. Additional properties of these functions are also investigated.
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