We recall the construction of the Gromov-Hausdorff distance. We concentrate on quantitative aspects of the definition and on quantitative properties of the distance .

We prove that every homogeneous continuum is an open retract of a non-metric homogeneous indecomposable continuum. 0. Introduction. A continuum X is indecomposable if it cannot be written as the union of two proper subcontinua. Examples of 1-dimensional homogeneous indecomposable continua are the pseudo-arc and the solenoids. J. T. Rogers asked whether there is an example of a homogeneous indec...

Viglino defined a Hausdorff topological space to be C-compact if each closed subset of the space is anH-set in the sense of Velǐcko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S-set in the sense of Dickman and Krystock. Such spaces are calledC-s-compact. Recently, the notion of strongly subclosed relation, introduced by Jose...

Let E be a separable Banach space and Ω be a compact Hausdorff space. It is shown that the space C(Ω, E) has property (V) if and only if E does. Similar result is also given for Bochner spaces L(μ,E) if 1 < p < ∞ and μ is a finite Borel measure on Ω.

Introduction, Let © be the class of all countable and connected perfectly separable Hausdorff spaces containing more than one point. I t is known that an ©-space cannot be regular or compact. Urysohn, using a complicated identification of points, has constructed the first example of an ©-space. Two ©-spaces, X and X*, more simply constructed and not involving identifications, are presented here...

Themain aim of this paper is to provide a construction of the Banaschewski compactification of a zero-dimensional Hausdorff topological space as a structure space of a ring of ordered field-valued continuous functions on the space, and thereby exhibit the independence of the construction from any completeness axiom for an ordered field. In the process of describing this construction we have gen...

In this paper we generalize the notion of perfect compactification of a Tychonoff space to a generic extension of any space by introducing the concept of perfect pair. This allow us to simplify the treatment in a basic way and in a more general setting. Some [S1], [S2], and [D]’s results are improved and new characterizations for perfect (Hausdorff) extensions of spaces are obtained.

Our concern will be mainly with the case where G/H is a homogeneous space of reductive type (Definition 5). If H is not compact, the action of a discrete subgroup Γ of G on G/H is not automatically properly discontinuous and the double coset Γ\G/H may be non-Hausdorff. This fact is the main difficulty in our problem. In fact, it may well happen that only finite subgroups of G can act properly d...

There is a locally compact Hausdorff space of weight אω which is linearly Lindelöf and not Lindelöf.