|54B15||Quotient spaces, decompositions|
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
endowed with compact-open topology τco, where βD is the Stone-Čech-compactification of
a discrete space.