We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche.

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...

If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped with the compact-open topology. For subsets A and B of X we define [A, B] = {h ∈ H(X) : h(A) ⊂ B}, and we recall that the topology on H(X) is generated by the subbasis SX = {[K , O] : K compact, O open in X}. If X is a compact Hausdorff space, then H(X) is a topological group, that is, composition...

This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7̂ ) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation. The topic of compactification poses an obvious challenge to this programme, since only a Tychonoff space can h...

In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique uppercontinuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a compact space, and to prove the existence of an upper-continuous capacity on the product space of infinite...

We prove some closed mapping theorems on k-spaces with point-countable k-networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space Ur with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a k-space X with a point-countable k-network admitting a closed surjection which is not compac...

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...

It is known that a real valued measure (1) on the a-ring of Baire sets of a locally compact Hausdorff space, or (2) on the Borel sets of a complete separable metric space is regular. Recently Dinculeanu and Kluvanek used regularity of non-negative Baire measures to prove that any Baire measure with values in a locally convex Hausdorff topological vector space (TVS) is regular. Subsequently a di...

A continuum is a compact connected Hausdorff space. If X is a continuum, then CEX is a C-set if (i) C^X, (ii) for each subcontinuum A EX that meets C we have either A EC or CEA. Thus a composant of a solenoid is a C-set. A ?«0& is a Hausdorff space together with a continuous associative multiplication. A clan is a compact connected mob with (two-sided) unit, denoted by u. In what follows we ass...