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H-closed extensions with countable remainder

Daniel K. McNeill (2012)

Commentationes Mathematicae Universitatis Carolinae

This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension with countable remainder. In particular,...

H-closed functions

Filippo Cammaroto, Vitaly V. Fedorcuk, Jack R. Porter (1998)

Commentationes Mathematicae Universitatis Carolinae

The notion of a Hausdorff function is generalized to the concept of H-closed function and the concept of an H-closed extension of a Hausdorff function is developed. Each Hausdorff function is shown to have an H-closed extension.

Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations

Boaz Tsaban, Lubomyr Zdomsky (2012)

Journal of the European Mathematical Society

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property hereditarily. We proceed to consider the class of Arhangel’skii α 1 spaces, for which every sheaf at a point can be amalgamated in a natural way. Let C p ( X ) denote the space of continuous real-valued functions on X with the topology of pointwise convergence. Our main result...

Hereditarily indecomposable inverse limits of graphs

K. Kawamura, H. M. Tuncali, E. D. Tymchatyn (2005)

Fundamenta Mathematicae

We prove the following theorem: Let G be a compact connected graph and let f: G → G be a piecewise linear surjection which satisfies the following condition: for each nondegenerate subcontinuum A of G, there is a positive integer n such that fⁿ(A) = G. Then, for each ε > 0, there is a map f ε : G → G which is ε-close to f such that the inverse limit ( G , f ε ) is hereditarily indecomposable.

Hereditarily non-sensitive dynamical systems and linear representations

E. Glasner, M. Megrelishvili (2006)

Colloquium Mathematicae

For an arbitrary topological group G any compact G-dynamical system (G,X) can be linearly G-represented as a weak*-compact subset of a dual Banach space V*. As was shown in [45] the Banach space V can be chosen to be reflexive iff the metric system (G,X) is weakly almost periodic (WAP). In the present paper we study the wider class of compact G-systems which can be linearly represented as a weak*-compact subset of a dual Banach space with the Radon-Nikodým property. We call such a system a Radon-Nikodým...

Hereditarily normal Katětov spaces and extending of usco mappings

Ivailo Shishkov (2000)

Commentationes Mathematicae Universitatis Carolinae

Several classes of hereditarily normal spaces are characterized in terms of extending upper semi-continuous compact-valued mappings. The case of controlled extensions is considered as well. Applications are obtained for real-valued semi-continuous functions.

Hereditarily weakly confluent induced mappings are homeomorphisms

Janusz Charatonik, Włodzimierz Charatonik (1998)

Colloquium Mathematicae

For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.

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