A Product Theorem in Dimension.
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark on the equivalence of certain dimension functions
A study of universal elements in classes of bases of topological spaces
The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in “Universal spaces and mappings” by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in “A topological dimension greater than or equal to the classical covering dimension” by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which...
A subset theorem in dimension theory
A sum theorem for A-weakly infinite-dimensional spaces
A transfinite extension of the covering dimension
A universal separable metric locally finite-dimensional space
A Z-set unknotting theorem for Nöbeling spaces
We prove a Z-set unknotting theorem for Nöbeling spaces.
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.
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 every function is independent
An algebraic and logical approach to continuous images
An alternative concept of the n-dimensional measure
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 infinitary version of Sperner's Lemma
We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.
An n-dimensional compactum which remains n-dimensional after removing all Cantor n-manifolds
An n-dimensional version of Wage's example
ANR's and NES's in the category of mappings on metric spaces