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1
Content available Boolean algebra of one-point local compactifications
Polański Artur
Journal of Mathematics and Applications
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2020
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Vol. 43
113--121
EN
For a given locally compact Hausdorff space we introduce a Boolean algebra structure on the family of all its one-point local compactifications.
2
Content available remote Some applications of minimal Pγ-open sets
Khalaf A. B., Ibrahim H. Z.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
423--432
EN
We characterize minimal Pγ-open sets in topological spaces. We show that any nonempty subset of a minimal Pγ-open set is pre Pγ-open. As an application of a theory of minimal Pγ-open sets, we obtain a sufficient condition for a Pγ-locally finite space to be a pre Pγ-Hausdorff space.
3
Content available remote Rδ-supercontinuous functions
Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.
Demonstratio Mathematica
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2014
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Vol. 47, nr 2
433--448
EN
A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).
4
Content available remote The Demyanov metric and measurable multifunctions
Leśniewski A.
Journal of Mathematics and Applications
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2010
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Vol. 33
61-65
EN
We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.
5
Breakthrough in Interval Data Fitting I. The Role of Hausdorff Distance
Gutowski M.W.
Prace Naukowe Politechniki Warszawskiej. Elektronika
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2009
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z. 169
63-72
EN
This is the first of two papers describing the process of fitting experimental data under interval uncertainty. Probably the most often encountered application of global optimization methods is finding the so called best fitted values of various parameters, as well as their uncertainties, based on experimental data. Here I present the methodology, designed from the very beginning as an interval-oriented tool, meant to replace to the large extent the famous Least Squares (LSQ) and other slightly less popular methods. Contrary to its classical counterparts, the presented method does not require any poorly justified prior assumptions, like smallness of experimental uncertainties or their normal (Gaussian) distribution. Using interval approach, we are able to fit rigorously and reliably not only the simple functional dependencies, with no extra effort when both variables are uncertain, but also the cases when the constitutive equation exists in implicit rather than explicit functional form. The magic word and a key to success of interval approach appears the Hausdorff distance.
6
Content available remote Remarks on connectivity and I-connectivity
Jędrzejewski J., Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
49-54
7
Content available remote Countable compact scattered T2 spaces and weak forms of AC
Keremedis K., Felouzis E., Tachtsis E.
Bulletin of the Polish Academy of Sciences. Mathematics
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2006
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Vol. 54, no 1
75-84
EN
We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T2 topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T2 space is scattered iff it is metrizable. (3) If the real line R can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional T2 space is scattered. (4) It is not provable in ZF+¬AC that there exists a countable compact T2 space which is dense-in-itself.
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