-абсолют и интегрируемые по Риману функции.
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А.В. Колдунов (1987)
Sibirskij matematiceskij zurnal
Donald Plank (1969)
Fundamenta Mathematicae
Jan Hejcman (1987)
Commentationes Mathematicae Universitatis Carolinae
Oleg Okunev (1993)
Commentationes Mathematicae Universitatis Carolinae
We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a -analytic space under a measurable mapping. We also obtain characterizations of analyticity and -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if is a separable metrizable space and is its dense subspace then the space of restricted continuous functions is analytic iff it is a -space iff is -compact.
Angelo Bella, Ivan V. Yashchenko (1999)
Commentationes Mathematicae Universitatis Carolinae
Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) over -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while...
Eiichi Matsuhashi (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
We characterize Peano continua using Bing-Krasinkiewicz-Lelek maps. Also we deal with some topics on Whitney preserving maps.
Yang, J.S. (1980)
International Journal of Mathematics and Mathematical Sciences
Takashi Kimura, Kazuhiko Morishita (2002)
Fundamenta Mathematicae
We prove that, for every finite-dimensional metrizable space, there exists a compactification that is Eberlein compact and preserves both the covering dimension and weight.
Masami Sakai (1992)
Commentationes Mathematicae Universitatis Carolinae
A.V. Arkhangel’skii asked that, is it true that every space of countable tightness is homeomorphic to a subspace (to a closed subspace) of where is Lindelöf? denotes the space of all continuous real-valued functions on a space with the topology of pointwise convergence. In this note we show that the two arrows space is a counterexample for the problem by showing that every separable compact linearly ordered topological space is second countable if it is homeomorphic to a subspace of ...
K. Alster, Roman Pol (1980)
Fundamenta Mathematicae
Ingo Bandlow (1994)
Commentationes Mathematicae Universitatis Carolinae
We apply elementary substructures to characterize the space for Corson-compact spaces. As a result, we prove that a compact space is Corson-compact, if can be represented as a continuous image of a closed subspace of , where is compact and denotes the canonical Lindelöf space of cardinality with one non-isolated point. This answers a question of Archangelskij [2].
Jäger, Gunther (1999)
International Journal of Mathematics and Mathematical Sciences
Juan Carlos Ferrando (2014)
Studia Mathematica
It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.
A. Bouziad, E. Sukhacheva (2017)
Commentationes Mathematicae Universitatis Carolinae
For a subset of the real line , Hattori space is a topological space whose underlying point set is the reals and whose topology is defined as follows: points from are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on which are sufficient and necessary for to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in...
Hisao Kato (2015)
Commentationes Mathematicae Universitatis Carolinae
In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces and , where and denote the Hilbert cube and a Cantor set, respectively.
Sánchez Ruiz, L.M., López Pellicer, M. (1991)
Portugaliae mathematica
Taras O. Banakh, Volodymyr Mykhaylyuk, Lubomyr Zdomsky (2011)
Commentationes Mathematicae Universitatis Carolinae
For a non-isolated point of a topological space let be the smallest cardinality of a family of infinite subsets of such that each neighborhood of contains a set . We prove that (a) each infinite compact Hausdorff space contains a non-isolated point with ; (b) for each point with there is an injective sequence in that -converges to for some meager filter on ; (c) if a functionally Hausdorff space contains an -convergent injective sequence for some meager filter...
McMaster, T.B.M. (1990)
International Journal of Mathematics and Mathematical Sciences
Witold Marciszewski (1995)
Studia Mathematica
We construct an example of a Banach space E such that every weakly compact subset of E is bisequential and E contains a weakly compact subset which cannot be embedded in a Hilbert space equipped with the weak topology. This answers a question of Nyikos.
T. Maćkowiak (1976)
Colloquium Mathematicae
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