منابع مشابه
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...
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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...
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In this paper examples are given to show that s-regular and s-normal are independent; that s-normal, and s-regular are not semi topological properties; and that (S(X),E(X)) need not be I even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X) ,E(X)), (S(XO) ,E(Xo)), and (S(Xs0) ,E(Xs0)) are homeomorphic, where (X0, Q(X0)) is the T0-iden...
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We consider the uniform hyperspaces of a uniform space X, its associated Hausdorff space sX and its Hausdorff completion nX, and investigate the relationships between the functors s and n and the various hyperspace functors. Thus Theorem 1 says that there is a natural isomorphism between the functors TTE and TTETT, where ii'A'is the space of non-empty closed subsets of X, endowed with the Hausd...
متن کاملSubbases, Convex Sets, and Hyperspaces
S[ and Sg are then said to separate (or: to screen) S± and S2. Finally, Sf is called a binary subbase if each linked system S^ (zS^ (i.e., a subcollection S^' of ^ of which any two members meet) satisfies ς\Sf'φ 0. It is well-known that a binary subbase is TΊ (cf. van Mill [9, Lemma 1]), that a space carrying a binary subbase is compact (use Alexander's lemma), and that a space is completely re...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1986
ISSN: 0166-8641
DOI: 10.1016/0166-8641(85)90040-9