One possible natural monotone version of countable paracompactness, MCP, turns out to have some interesting properties. We investigate various other possible monotonizations of countableâ€¦ (More)

We provide new proofs for the classical insertion theorems of Dowker and Michael. The proofs are geometric in nature and highlight the connection with the preservation of normality in products. Bothâ€¦ (More)

We prove that, if there is a model of set-theory which contains no first countable, locally compact, scattered Dowker spaces, then there is an inner model which contains a measurable cardinal. Aâ€¦ (More)

We look at density of periodic points and Devaney Chaos. We prove that if f is Devaney Chaotic on a compact metric space with no isolated points, then the set of points with prime period at least nâ€¦ (More)

If f is an autohomeomorphism of some space X, then Î²f denotes its Stone-ÄŒech extension to Î²X. For each n â‰¤ Ï‰, we give an example of a first countable, strongly zerodimensional, subparacompact X and aâ€¦ (More)

We revisit van Dalen and Wattelâ€™s characterization of linearly ordered topological spaces in terms of nests of open sets and use this to give a topological characterization of ordinals. In particularâ€¦ (More)

We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space X, whose Tychonoff square is a Dowker space, then there isâ€¦ (More)

Given a map T : X â†’ X on a set X we examine under what conditions there is a separable metrizable or an hereditarily LindelÃ¶f or a LindelÃ¶f topology on X with respect to which T is a continuous map.â€¦ (More)

According to Mack a space is countably paracompact if and only if its product with [0, 1] is Î´-normal, i.e. any two disjoint closed sets, one of which is a regular GÎ´-set, can be separated. Inâ€¦ (More)