On n-fold hyperspaces of continua

Hyperspaces of Peano continua of euclidean spaces

If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space L(R) is homeomorphic to B∞, where B denotes the pseudo-boundary of the Hilbert cube Q. Introduction. For a space X, C(X) denotes the hyperspace of all nonempty subcontinua of X. It is known that for a Peano continuum X without free arcs, C(X) ≈ Q, where Q denotes the H...

HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2XAND Cn(X)

Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, C...

n-fold Commutative Hyper K-ideals

 In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

SOME THEOREMS ON n-HOMOGENEOUS CONTINUA

CONCERNING n-MUTUAL APOSYNDESIS IN HYPERSPACES

Given a metric continuum X, let 2 denote the hyperspace of nonempty closed subsets of X. We prove that 2 is n-mutually aposyndetic for each n ≥ 1. That is, given n distinct elements of 2 , there are n disjoint subcontinua of 2 , each containing one of the elements in