Abstract distance and neighborhood spaces
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Accessibility spaces, -spaces and initial topologies
Accumulation points of nowhere dense sets
Acknowledgement concerning two papers on rational dimension
Acknowledgment to the paper: “Another proof that a chain of non-empty -closed subspaces has a non-empty intersection’
Action of topological semigroups, invariant means, and fixed points
Actions by a bisimple w-semigroup.
Actions, functors and the bar construction
Actions of a locally compact group with zero II.
Actions of a noncompact semigroup with zero.
Acyclic Maps and Knot Complements.
Addendum to "A survey of semigroups of continuous selfmaps" (with intro. by K. D. Magill).
Addendum to completion and closure
Addendum to the paper: “Some fixed point theorems for multivalued mappings”
Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom
Adding machines, endpoints, and inverse limit spaces
Let f be a unimodal map in the logistic or symmetric tent family whose restriction to the omega limit set of the turning point is topologically conjugate to an adding machine. A combinatoric characterization is provided for endpoints of the inverse limit space (I,f), where I denotes the core of the map.
Addition and subspace theorems for asymptotic large inductive dimension
We prove the addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.
Addition theorems and -spaces
It is proved that if a regular space is the union of a finite family of metrizable subspaces then is a -space in the sense of E. van Douwen. It follows that if a regular space of countable extent is the union of a finite collection of metrizable subspaces then is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a -space. Some other new results on the properties of spaces which are unions of a finite collection of nice subspaces...
Addition theorems, -spaces and dually discrete spaces
A neighbourhood assignment in a space is a family of open subsets of such that for any . A set is a kernel of if . If every neighbourhood assignment in has a closed and discrete (respectively, discrete) kernel, then is said to be a -space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf -space is a -space and we prove an addition...