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...
Alexandroff topologies viewed as closed sets in the Cantor cube.
Algebraic properties of quasi-finite complexes
A countable CW complex K is quasi-finite (as defined by A. Karasev) if for every finite subcomplex M of K there is a finite subcomplex e(M) such that any map f: A → M, where A is closed in a separable metric space X satisfying XτK, has an extension g: X → e(M). Levin's results imply that none of the Eilenberg-MacLane spaces K(G,2) is quasi-finite if G ≠ 0. In this paper we discuss quasi-finiteness of all Eilenberg-MacLane spaces. More generally, we deal with CW complexes with finitely many...
Algebraic theory of fundamental dimension [Book]
Almost convex metrics and Peano compactifications.
Almost every function is independent
Almost metric versions of Zhong's variational principle
An acyclic continuum that admits no mean
An algebraic and logical approach to continuous images
An alternative concept of the n-dimensional measure
An application of peripherality to compact semigroups.
An approach to covering dimensions
Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.
An arcwise connected continuum without nonboundary proper arcwise connected subcontinua.
An atomic map onto an arbitrary metric continuum
An atriodic tree-like continuum with positive span
An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum
An embedding theorem for semigroups of continuous selfmaps.
An Exactly Two-to-One Map from an Indecomposable Chainable Continuum
It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.
An example concerning the Whitehead Theorem in shape theory