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The convergence space of minimal usco mappings

R. Anguelov, O. F. K. Kalenda (2009)

Czechoslovak Mathematical Journal

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all...

The dual form of Knaster-Kuratowski-Mazurkiewicz principle in hyperconvex metric spaces and some applications

George Isac, George Xian-Zhi Yuan (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we first establish the dual form of Knaster- Kuratowski-Mazurkiewicz principle which is a hyperconvex version of corresponding result due to Shih. Then Ky Fan type matching theorems for finitely closed and open covers are given. As applications, we establish some intersection theorems which are hyperconvex versions of corresponding results due to Alexandroff and Pasynkoff, Fan, Klee, Horvath and Lassonde. Then Ky Fan type best approximation theorem and Schauder-Tychonoff fixed point...

The homotopies of admissible multivalued mappings

Mirosław Ślosarski (2012)

Open Mathematics

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.

The intersection convolution of relations and the Hahn-Banach type theorems

Árpád Száz (1998)

Annales Polonici Mathematici

By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...

The Lindelöf number greater than continuum is u-invariant

Arbit, A. V. (2011)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.Two Tychonoff spaces X and Y are said to be l-equivalent (u-equivalent) if Cp(X) and Cp(Y) are linearly (uniformly) homeomorphic. N. V. Velichko proved that countable Lindelöf number is preserved by the relation of l-equivalence. A. Bouziad strengthened this result and proved that any Lindelöf number is preserved by the relation of l-equivalence. In this paper it has been proved that the Lindelöf number greater than continuum is preserved...

Tightness of compact spaces is preserved by the t -equivalence relation

Oleg Okunev (2002)

Commentationes Mathematicae Universitatis Carolinae

We prove that if there is an open mapping from a subspace of C p ( X ) onto C p ( Y ) , then Y is a countable union of images of closed subspaces of finite powers of X under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if X and Y are t -equivalent compact spaces, then X and Y have the same tightness, and that, assuming 2 𝔱 > 𝔠 , if X and Y are t -equivalent compact spaces and X is sequential, then Y is sequential.

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