Let m be a Radon measure on a Hausdorff topological space X. Corresponding to three kinds of outer measures, three kinds of m-negligible sets are considered. The main theorem states that in a metacompact space X each locally m-negligible set is m-negligible. For a Radon measure in a HausdorfT topological space X we distinguish three kinds of negligible sets corresponding to three kinds of outer...

A Dowker space (that is, a normal space that is not countably metacompact) is constructed which is also screenable and the countable union of discrete subspaces. The construction and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modification in a new exposition with several new results common to the two spaces, i...

in proposition 2.6 in (g‎. ‎gruenhage‎, ‎a‎. ‎lutzer‎, ‎baire and volterra spaces‎, ‎textit{proc‎. ‎amer‎. ‎math‎. ‎soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $d$ is $g_delta$ in $x$ was overlooked‎. ‎so we‎ ‎proved some conditions by which a baire space is equivalent to a‎ ‎volterra space‎. ‎in this note we show that if $x$ is a‎ ‎monotonically normal $t_1$...

Dowker spaces (that is, normal spaces that are not countably metacompact) are constructed which are also screenable and the countable union of discrete subspaces. The constructions and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modifications in a new exposition with several new results common to these spaces, ...

In this paper we examine the role of the β-space property (equivalently of the MCM-property) in generalized ordered (GO-)spaces and, more generally, in monotonically normal spaces. We show that a GO-space is metrizable iff it is a β-space with a Gδ-diagonal and iff it is a quasidevelopable β-space. That last assertion is a corollary of a general theorem that any β-space with a σ-point-finite ba...

a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...

In this paper we investigate the role of domain representability and Scott-domain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α (= the non-empty player) in the strong Ch...