Functional Analysis and its Applications by Vladimir Kadets and Wiestaw Źelazko (Eds.)

By Vladimir Kadets and Wiestaw Źelazko (Eds.)

The convention happened in Lviv, Ukraine and used to be devoted to a recognized Polish mathematician Stefan Banach f{ the main awesome consultant of the Lviv mathematical tuition. Banach areas, brought through Stefan Banach at first of 20th century, are general now to each mathematician. The ebook features a brief historic article and medical contributions of the convention individuals, in most cases within the components of sensible research, normal topology, operator idea and comparable issues.

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For such spaces we have the following result proven in [10], see also [24]. 2. Each monotone tt-space has the weak Skorokhod property. 2 is a weakening of the strong Skorokhod property for uniformly tight weakly convergent sequences of Radon measures. It is clear that the above defined Skorokhod properties have a sequential nature. So we recall some concepts related to sequences and sequentiality. A subset U of a topological space X is called a sequential neighborhood of a point x € X if for each sequence (xn) C X convergent to x there is n £ N such that xm £ U for all m > n (in [25] sequential neighborhoods are called sequential barriers).

D. ,hd) £ (OjTrn^"1) x . . x (OjTrn^ 1 ). ,2-KidnZ1) Cl 1 is Q'L---optimal / r i , . . ,/i . For the class W7"^;"'1 Q^-optimality of q~ was in particular proved in [6]. Theorem 1 can be used for extending results on optimization of one-dimensional quadrature formulae with non-overlapping intervals or fixed nodes to the case of cubature formulae with non-overlapping node parallelepipeds or nodes at a fixed net. One can also use it to obtain optimal cubature formulae for some classes of the form ( Y j , .

Following [2] and [3] we say that a topological space X is an a^-space if for any countable family {£„} of sequences convergent to a point x G X, there is a sequence rj that converges to x and meets infinitely many sequences £ n . 191]). A topological space is strong Frechet if and only if it is a Frechet-Urysohn o^-space. A function / : X —> Y between topological spaces is sequentially continuous if for each convergent sequence (xn) C X the sequence (f(xn)) is convergent and lim/(a; n ) = / ( l i m x n ) .

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