In this paper we study the extending of the Matheron theorem for general topological spaces. We also show some examples about the spaces F such that the miss-and-hit topology on those spaces are unseparated or non-Hausdorff.
1. Introduction The Choquet theorem (see [1, 2]) plays very importance role in theory of random sets. The proof of this theorem is based on the Matheron theorem and especially, the locally compact property of the space F , where F is a space of all close subsets of a given space E and F is equipped with the miss-and-hit topology (see ). ...
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces
Classical differential geometry is the approach to geometry that takes full
advantage of the introduction of numerical coordinates into a geometric
space. This use of coordinates in geometry was the essential insight of Rene
Descartes that allowed the invention of analytic geometry and paved the way
for modern differential geometry. The basic object in differential geometry
(and differential topology) is the smooth manifold. This is a topological
space on which a sufficiently nice family of coordinate systems or "charts"
This is the second volume containing examples from Functional analysis. The topics here are
limited to Topological and metric spaces, Banach spaces and Bounded operators.
Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author
has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors
which do occur in the text.
The book before the reader is devoted to an exposition of results of investigations
carried out mainly over the last 10-15 years concerning certain
questions in the theory of quasiconformal mappings.
The principal objects of investigation-mappings with bounded distortion-
are a kind of n-space analogue of holomorphic functions. As is
known, every holomorphic function is characterized geometrically by the
fact that the niapping of a planar domain it implements is conformal. In
the n-space case the condition of conformality singles out a very narrow
class of mappings.
Annals of Mathematics
This paper is the third in a series where we describe the space of all embedded minimal surfaces of ﬁxed genus in a ﬁxed (but arbitrary) closed 3-manifold. In [CM3]–[CM5] we describe the case where the surfaces are topologically disks on any ﬁxed small scale. Although the focus of this paper, general planar domains, is more in line with [CM6], we will prove a result here (namely, Corollary III.
We study “ﬂat knot types” of geodesics on compact surfaces M 2 . For every ﬂat knot type and any Riemannian metric g we introduce a Conley index associated with the curve shortening ﬂow on the space of immersed curves on M 2 . We conclude existence of closed geodesics with prescribed ﬂat knot types, provided the associated Conley index is nontrivial. 1. Introduction If M is a surface with a Riemannian metric g then closed geodesics on (M, g) are critical points of the length functional L(γ) = |γ (x)|dx deﬁned on the space of unparametrized C...
This is a quick set of note on basic differential topogoly. It get sketchier as it goes on. The last few section are only introduce the terminology and the some of concepts. These note qre written faster than I can read and may make no sense in spots.
In this paper we prove C k structural stability conjecture for unimodal maps. In other words, we shall prove that Axiom A maps are dense in the space of C k unimodal maps in the C k topology. Here k can be 1, 2, . . . , ∞, ω. 1. Introduction 1.1. The structural stability conjecture. The structural stability conjecture was and remains one of the most interesting and important open problems in the theory of dynamical systems. This conjecture states that a dynamical system is structurally stable if and only if it satisﬁes Axiom A and the...
We give a complete topological classiﬁcation of properly embedded minimal surfaces in Euclidian three-space. 1. Introduction In 1980, Meeks and Yau  proved that properly embedded minimal surfaces of ﬁnite topology in R3 are unknotted in the sense that any two such homeomorphic surfaces are properly ambiently isotopic. Later Frohman  proved that any two triply periodic minimal surfaces in R3 are properly ambiently isotopic.
Movies have always had a powerful influence on people’s
behavior, from how they talk to how they dress. Tobacco marketers
took advantage of this power to popularize cigarettes over cigars
and to make smoking by women socially acceptable.
The number of women stars posing with cigarettes in the
1930s and 1940s may have been no accident. And paying stars to
endorse cigarette brands in print and billboard advertising was
certainly business as usual, until smoking’s link to lung cancer
shattered tobacco’s glamorous image in the early 1960s....
(BQ) The book is largely about the Lebesgue theory of integration, but includes a very thorough coverage of the theory of metric and topological spaces in the first two chapters. Chapters 3,4 and 5 are the heart of the book covering measure theory, the Lebesgue integral and some topics from introductory functional analysis like theory of operators and Banach spaces.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Connectedness of approximate solutions set for vector equilibrium problems in Hausdorff topological vector spaces
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: TRANSFER POSITIVE HEMICONTINUITY AND ZEROS, COINCIDENCES, AND FIXED POINTS OF MAPS IN TOPOLOGICAL VECTOR SPACES
Another variation in the test train is the length of the test-based training
animals are standard presets for investigating space-time objects (such as 30
seconds total time of exploration, Frick & Gresack, 2003). A typical criteria include the
subjects taking the time to explore each stimulus during training. Interpretation may not be valid
be done if rodents do not understand fully both objects during training.