Hyperconnectivity of hyperspaces, Math.

Retraction properties of hyperspaces, Math.

Sup-characterization of stratifiable spaces (with G.

A study of absolute extensor spaces, Pacific J.

In this context, we consider the Zadeh’s extension f of f to F(X), the family of all. This result extends the Dugundji extension theorem, which in turn is a stronger version of the Tietze extension theorem. Given a metric space (X,d), we deal with a classical problem in the theory of hyperspaces: how some important dynamical properties (namely, weakly mixing, transitivity and point-transitivity) between a discrete dynamical system f:(X,d)&rarr (X,d) and its natural extension to the hyperspace are related. The same is true if Z is a closed, convex subset of a locally convex linear space. For example, he proved that a locally convex vector space X is an extensor space for stratifiable spaces, meaning that if Y is a stratifiable space and Z is a closed subspace, a continuous function from Y to X can be extended to Z. In the mathematical branch of topology, a hyperspace is a topological space, which consists of the set CL(X) of all closed subsets of another topological. Professor Borges has also considered questions of existence of extensions of continuous functions. He showed that a number of basic structure theorems about metrizable spaces, for example that the quotient of a first-countable metrizable space is metrizable, holds for stratifiable spaces also. In several papers, Professor Borges developed the notion of stratifiable spaces, which includes many relatively tame spaces which are too big to be metrizable. The study of these general spaces is called general topology and it has connections to analysis and logic. Such a structure is called a topology or a topology of open sets. Pettey (received 22 February, 1982) A topological space is Ri) H(i), feebly compact if every. However, many of the ideas of topology are still useful when one considers spaces have the bare minimum structure needed to define continuity. The most common objects in topology, such as manifolds, polyhedra, and Euclidean spaces, are metrizable spaces, which means that one can describe the topology by a (real-valued) distance between points, and say that a sequence of points converges to a limit if and only if the distance decreases to zero. In particular, he is interested in stratifiable spaces and other spaces which have some but not all properties of metrizable spaces. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. more stack exchange communities company blog. Math., 47(1973), 553-565.Professor Carlos Borges' research is in the area of general topology, the study of highly abstracted topological spaces. Sign up or log in to customize your list. Schirmer, On fixed point sets of homeomorphisms of the n-ball, Israel J. Schirmer, Fixed point sets of homeomorphisms of compact surfaces, Israel J. Schirmer, Fixed point sets of continuous selfmaps, in: Fixed Point Theory, Conf. 49, Marcel Dekker, New York and Basel, 1978. Nadler Jr., Hyperspaces of sets: A text with research questions, Monographs and Textbooks, Pure Appl.

Weiss, Fixed point sets of metric and nonmetric spaces, Trans. Tymchatyn, Fixed point sets of products and cones, Pacific J. Nadler Jr., Examples and questions in the theory of fixed point sets, Canad. Journal of the London Mathematical Society, Volume s2-12, Issue 4. Martin, Fixed point sets of homeomorphisms of metric products, Proc. We consider the uniform hyperspaces of a uniform space X, its associated Hausdorff. Curtis, Hyperspaces of noncompact metric spaces, Compositio Mathematica, 40(1980), 126-130. Martin, Compact groups and fixed point sets, Trans. Bredon, Introduction to Compact Transformation Groups, Academic Press, New York, London, 1972. Voytsitskyy, Characterizing metric spaces whose hyperspaces are absolute neighborhood retracts, Topology Appl., 154(2007), 2009-2025. Nadler, Jr., Whitney levels in hyperspaces of certain Peano continua, Trans. Srivastava, On S-equivariant complete invariance property, Journal of the Indian Math. Antonyan, West's problem on equivariant hyperspaces and Banach-Mazur compacta, Trans.

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