A Theorem On Spaces 2X With The Compact-Open Topology
A theorem on spaces 2x with the compact-open topology.
A theorem on the weak topology of C(X) for compact scattered X
A theory of absolute proper retracts
A tiny peculiar Fréchet space
A topological application of flat morasses
We define combinatorial structures which we refer to as flat morasses, and use them to construct a Lindelöf space with points of cardinality , consistent with GCH. The construction reveals, it is hoped, that flat morasses are a tool worth adding to the kit of any user of set theory.
A topological collapse number for all spaces
A Topological Notion of Boundedness.
A topological property of beta(N).
A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement
We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.
A topological version of a combinatorial theorem of Katětov
A topology generated by eventually different functions
A Tychonoff non-normal space.
A type of βN with relative types
A unified theory of weak separation properties.
A universal metacompact developable -space of weight m
A variant of a theorem of Sierpiński concerning partitions of continua
A very general covering property
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are shown to be equivalent to a covering property in the sense considered here (Corollary 3.10). Conversely, every covering property is equivalent to the existence of appropriate kinds of accumulation points for arbitrary sequences on some fixed index set (Corollary 3.5)....
A weakening of , with applications to topology
A weakly pseudocompact subspace of Banach space is weakly compact