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1
Content available remote On a weak form of almost weakly continuous functions
100%
Baker C.
Demonstratio Mathematica
|
2000
|
tom 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.
2
Content available remote Topological Characterisation of Multi-Buffer Simulation
100%
Hutagalung M.
Fundamenta Informaticae
|
2021
|
tom 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.
3
Content available On the almost uniform convergence
80%
Drozdowski R. , Jędrzejewski J. , Sochaczewska A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2013
|
tom 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.
4
Content available remote Maximal classes for the family of quasi-continuous functions with closed graph
80%
Sieg W.
Demonstratio Mathematica
|
2009
|
tom 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.
5
Content available remote Perfectly continuous functions
80%
Kohli J. , Singh D.
Demonstratio Mathematica
|
2009
|
tom 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.
6
Content available remote F. Riesz Theorem
80%
Narita K. , Nakasho K. , Shidama Y.
Formalized Mathematics
|
2017
|
tom 25
|
nr 3
179-184
EN
In this article, we formalize in the Mizar system [1, 4] the F. Riesz theorem. In the first section, we defined Mizar functor ClstoCmp, compact topological spaces as closed interval subset of real numbers. Then using the former definition and referring to the article [10] and the article [5], we defined the normed spaces of continuous functions on closed interval subset of real numbers, and defined the normed spaces of bounded functions on closed interval subset of real numbers. We also proved some related properties. In Sec.2, we proved some lemmas for the proof of F. Riesz theorem. In Sec.3, we proved F. Riesz theorem, about the dual space of the space of continuous functions on closed interval subset of real numbers, finally. We applied Hahn-Banach theorem (36) in [7], to the proof of the last theorem. For the description of theorems of this section, we also referred to the article [8] and the article [6]. These formalizations are based on [2], [3], [9], and [11].
7
Content available remote On almost weakly continuous functions
80%
Jafari S. , Noiri T.
Demonstratio Mathematica
|
1998
|
tom Vol. 31, nr 2
437-443
8
Content available Baire measurability of \((M,N)\)-Wright convex functions
70%
Lewicki M.
Commentationes Mathematicae
|
2008
|
tom 48
|
nr 1
EN
Let \(I \subset \mathbb{R}\) be an open interval and \(M, N \colon I^2 \to I\) be means on \(I\). Let \(\varphi\colon I \to \mathbb{R}\) be a solution of the functional equation \[ \varphi(M (x, y)) + \varphi(N (x, y)) = \varphi(x) + \varphi(y),\quad x, y \in I \] We give sufficient conditions on \(M, N\) and the function \(\varphi\) such that for every Baire measurable solution \(f \colon I \to \mathbb{R}\) of the functional inequality \[ f (M (x, y)) + f (N (x, y)) \leq f (x) + f (y),\quad x, y \in I, \] the function \(f \circ \varphi^{-1} \colon \varphi(I) \to \mathbb{R}\) is convex.
9
Content available remote Baire measurability of (M,N)-Wright convex functions
70%
Lewicki M.
Commentationes Mathematicae
|
2008
|
tom 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].
10
Content available remote On some forms of weakly continuous functions in bitopological spaces
70%
Noiri T. , Popa V.
Demonstratio Mathematica
|
2008
|
tom 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.
11
Content available remote Characterization of continuous functions by class C(infinity) curves
60%
Najdecki A. , Tabor J.
Demonstratio Mathematica
|
2005
|
tom 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.
12
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
60%
Noiri T. , Popa V.
Demonstratio Mathematica
|
2005
|
tom 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.
13
Content available On monotonicity of real functions
60%
Jędrzejewski J. M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2017
|
tom 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.
14
Content available A note on weakly ϱ-upper continuous functions
60%
Nowakowska K. , Turowska M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
tom 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.
15
Content available Some algebraic properties of preponderantly continuous functions
60%
Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2011
|
tom 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.
16
Content available remote On an extension for functions
60%
Ekici E.
Demonstratio Mathematica
|
2006
|
tom 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.
17
Content available Uwagi o ewolucji pojęcia ciągłości
60%
Gawron P.
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2021
|
tom 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.
18
Content available Comparison of ψ -sparse topologies
60%
Goździewicz-Smejda A. , Łazarow E.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
tom 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.
19
Content available remote On the maxima of two functions which are simultaneously unilaterally approximately continuous and approximately regulated
51%
Grande M.
Demonstratio Mathematica
|
2005
|
tom 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.
20
Content available remote On the notion of (gamma, s)-continuous functions
51%
Ekici E.
Demonstratio Mathematica
|
2005
|
tom 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.
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