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1.
I. Dochviri 《Ukrainian Mathematical Journal》2006,58(12):1955-1960
Some properties of regular and normal bitopological spaces are established. The classes of sets inheriting the bitopological
properties of regularity and normality are found. A theorem on a finite covering of pairwise normal spaces is proved. We also
study the behavior of individual multivalued mappings, taking the axioms of bitopological regularity and normality into account.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1720–1724, December, 2006. 相似文献
2.
A. A. Ivanov 《Journal of Mathematical Sciences》2000,98(5):509-616
The paper is, in essence, a monograph devoted to the theory of bitopological spaces and its applications. Not exhausting the
entire subject, it reflects basic ideas and methods of the theory. The Introduction gives an idea of the origins of the basic
notions, contents, methods, and problems both of the classical (in the spirit of Kelly) and of the general theory of bitopological
spaces. The classical theory is described rather schematically in Chapter I, only the theory of extensions of topological
and bitopological spaces and the theory of completion of uniform spaces are presented in more detail. The main focus is on
the general theory of bitopological spaces (Chapter II). Notions, methods, and results presented here have no analogues in
the classical theory. As applications, foundations of the theory of bitopological manifolds, in particular, bitopologically
represented piecewise linear manifolds (Chapter III), and the foundations of the theory of bitopological groups are presented
(Chapter IV).
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 242, 1997, pp. 7–216.
Translated by A. A. Ivanov. 相似文献
3.
N. V. Khmylko 《Journal of Mathematical Sciences》2000,98(5):624-627
The notion of exactness of topological extensions is generalized to bitopological spaces, and some bitopological notions of
similar type are considered.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 242, 1997, pp. 230–236.
Translated by N. Yu. Netsvetaev. 相似文献
4.
A. A. Ivanov 《Journal of Mathematical Sciences》1996,81(2):2465-2496
This paper is the second part of a survey of recent results and new problems in the theory of bitopological spaces.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 208, 1993, pp. 5–67.
Translated by A. A. Ivanov. 相似文献
5.
A. A. Ivanov 《Journal of Mathematical Sciences》2000,98(5):617-623
The purpose of the paper is to extend the notions of splitting and jointly continuous topologies on function spaces to products
of spaces, to present a new theory of duality between topologies on function spaces and topologies on products of spaces,
and to generalize these theories to bitopological spaces. The author starts from the definitions well known in the literature.
Bibliography: 1 title.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 242, 1997, pp. 217–229.
Translated by N. Yu. Netsvetaev. 相似文献
6.
N. V. Morozova 《Journal of Mathematical Sciences》1998,91(6):3416-3419
Some connections and interrelations between Ti-separation axioms (i=1,2,3) for bitopological spaces are considered. In particular, four different versions of the definition
of the pairwise Hausdorff separation axion are discussed. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 135–140.
Translated by O. A. Ivanov. 相似文献
7.
《Quaestiones Mathematicae》2013,36(3):277-287
ABSTRACT The purpose of this paper is to investigate pairwise almost compact bitopological spaces. These spaces satisfy a bitopological compactness criterion which is strictly weaker than pairwise C-compactness and is independent of other well-known bitopological compactness notions. Pairwise continuous maps from such spaces to pairwise Hausdorff spaces are pairwise almost closed, the property is invariant under suitably continuous maps, is inherited by regularly closed subspaces and may be characterized in terms of certain covers as well as the adherent convergence of certain open filter bases. Some new natural bitopological separation axioms are introduced and in conjunction with pairwise almost compactness yield interesting results, including a sufficient condition for the bitopological complete separation of disjoint regularly closed sets by semi-continuous functions. 相似文献
8.
The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0, 1] was introduced by Martin (1980). Lin and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces. 相似文献
9.
The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces. 相似文献
10.
SeparationPropertiesofBitopologicalSpace¥TianLiqin(LuoyangAgricultralCollege)Abstract:Inthispaperwestudyabitopologicalspacewi... 相似文献
11.
We characterize pairwise Tychonoff bispaces that admit only totally bounded quasi-uniformities in terms of a suitable notion
of bitopological pseudocompactness. We also show that a pairwise Tychonoff bispace has a unique (up to equivalence) bicompactification
if and only if it admits a unique totally bounded quasi-unifomity. These results extend classical theorems of R. Doss for
uniform spaces to the quasi-uniform (bitopological) setting, and are applied to the study of T
0 topological spaces that admit a unique quasi-uniformity and a unique bicompactification, respectively. Finally, we discuss
the problem of extending the classical Glicksberg theorem on product of pseudocompact spaces to bispaces and a partial solution
is obtained.
Supported by the Spanish Ministry of Science and Technology, grant BFM2000-1111.
Supported by a grant from Generalitat Valenciana.
Received November 7, 2001; in revised form August 14, 2002 相似文献
12.
Gui Qiao XU Yong Sheng SUN Yong Ping LIU 《数学学报(英文版)》2006,22(6):1667-1678
In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel'fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively. 相似文献
13.
14.
Herz-type Triebel-Lizorkin Spaces, Ⅰ 总被引:1,自引:0,他引:1
Jing Shi XU Da Chun YANG 《数学学报(英文版)》2005,21(3):643-654
Let s ∈R,0〈β≤∞, 0〈 q, p〈 ∞ and-n/q〈α. In this paper the authors introduce the Herz-type Triebel-Lizorkin spaces,Kq^α,pFβ^s(R^n)andKq^α,pFβ^s(R^n)which are the generalizations of the well-known Herz-type spaces and the inhomogeneous Triebel-Lizorkin spaces, Some properties on these Herz-type Triebel Lizorkin spaces are also given. 相似文献
15.
R. S. Ismagilov 《Mathematical Notes》1997,62(2):186-197
We present simple proofs of the possibility of embedding ultrametric spaces in Hilbert spaces. The main part of the paper
deals with ultrametric spaces that we call totally infinite spaces. Related Hilbert spaces, automorphisms of totally infinite
spaces, and the corresponding linear operators are considered.
Transplated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 223–237, August, 1997.
Translated by V. E. Nazaikinskii 相似文献
16.
《Quaestiones Mathematicae》2013,36(2):203-207
Abstract Following a lead given by I.W. Alderton, it is shown that the MacNeille completion and the universal initial completion coincide for the categories of zero-dimensional fuzzy T0-topological spaces, T0-fuzzy closure spaces, 2T 0-fuzzy bitopological spaces, and T 1-fuzzy topological spaces and that these turn out to be respectively the categories of zero-dimensional fuzzy topological spaces, fuzzy closure spaces, fussy bitopological spaces, and fuzzy R 0 topological spaces. 相似文献
17.
V. I. Malykhin 《Mathematical Notes》1998,64(3):351-356
It is proved that the space of continuous functions on the ordinary closed interval with the topology of pointwise convergence
is not subsequential. In sequential spaces satisfying certain conditions, subspaces dense-in-themselves without convergent
sequences are found; such subspaces are constructed in certain sequential compact spaces and semitopological groups.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 407–413, September, 1998.
The author thanks the participants of Arkhangel'skii's seminar held at Moscow State University for useful discussions of this
work. 相似文献
18.
S. V. Astashkin 《Mathematical Notes》1999,65(1):3-12
In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered.
A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other
to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact
in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly
singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved.
Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999. 相似文献
19.
《Quaestiones Mathematicae》2013,36(7):877-888
AbstractIn this paper we continue previous investigations on the weaker forms of the Menger property in bitopological spaces. We introduce weakly Menger property and study some topological properties of almost and weakly Menger bitopological spaces. We also consider the almost Hurewicz spaces in a bitopological context. 相似文献
20.
H.M. Abu-Donia 《Journal of the Egyptian Mathematical Society》2013,21(3):318-323
In this paper, we introduce a new type of closed sets in bitopological space (X, τ1, τ2), used it to construct new types of normality, and introduce new forms of continuous function between bitopological spaces. Finally, we proved that the our new normality properties are preserved under some types of continuous functions between bitopological spaces. 相似文献