Alexandroff topologies viewed as closed sets in the Cantor cube.
Algebra in the superextensions of twinic groups [Book]
Algebraic and essentially algebraic composition operators on C(X).
Algebraic and topological structures on the set of mean functions and generalization of the AGM mean
We present new structures and results on the set of mean functions on a given symmetric domain in ℝ². First, we construct on a structure of abelian group in which the neutral element is the arithmetic mean; then we study some symmetries in that group. Next, we construct on a structure of metric space under which is the closed ball with center the arithmetic mean and radius 1/2. We show in particular that the geometric and harmonic means lie on the boundary of . Finally, we give two theorems...
Algebraic characterization of finite (branched) coverings
Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S) → C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched) covering, i.e., an open and closed map whose fibres are finite, if and only if the induced homomorphism...
Algebraic cohomology of compact monoids.
Algebraic de Morgan's laws for non-commutative rings
Algebraic generalization of the topological theorems of Bolzano and Weierstrass
Algebraic properties of function spaces
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 properties of rings of continuous functions
This paper is devoted to the study of algebraic properties of rings of continuous functions. Our aim is to show that these rings, even if they are highly non-noetherian, have properties quite similar to the elementary properties of noetherian rings: we give going-up and going-down theorems, a characterization of z-ideals and of primary ideals having as radical a maximal ideal and a flatness criterion which is entirely analogous to the one for modules over principal ideal domains.
Algebraic properties of the 3-state vector Potts model
Algebraic properties of the Lefschetz zeta function, periodic points and topological entropy.
The Lefschetz zeta function associated to a continuous self-map f of a compact manifold is a rational function P/Q. According to the parity of the degrees of the polynomials P and Q, we analyze when the set of periodic points of f is infinite and when the topological entropy is positive.
Algebraic representation of continua.
Algebraic structures generated by almost continuous functions
Algebraic theory of fundamental dimension [Book]
Algebraic Transformation Groups and Representation.
Algebraische Hüllenoperatoren, bei denen jede endliche Menge durch die Menge ihrer isolierten Elemente erzeugt wird
Algebras and spaces of dense constancies
A DC-space (or space of dense constancies) is a Tychonoff space such that for each there is a family of open sets , the union of which is dense in , such that , restricted to each , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...
Algebras of Borel measurable functions
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.