René Bartsch

Vietoris hyperspaces as quotients of natural function spaces

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 69, 55 - 66 (2014/15)

MSC: 54B20   Hyperspaces
  54C35   Function spaces
  54B15   Quotient spaces, decompositions

Abstract:   Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in theoretical computer sciences, for example (to illustrate the wide scope of this concept). Moreover, there are many connections between hyperspaces and function spaces in topology. Thus results from hyperspaces help to get new results in function spaces and vice versa. We give here a new description of the Vietoris hyperspace on the family K(Y) of the nonempty compact subsets of a regular topological space Y as quotient of the space C(βD, Y), endowed with compact-open topology τco, where βD is the Stone-Čech-compactification of a discrete space.

Keywords:   Hyperspaces, Function spaces, Quotient spaces, decompositions
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