8 citations · 8 across the 4 of their papers we have counts for
5 papers
The Tautness Property of Homology Theory
Anzor Beridze, Leonard Mdzinarishvili
The tautness for a cohomology theory is formulated and studied by various authors. However, the analogous property is not considered for a homology theory. In this paper, we will d…
On Axiomatic Characterization of Alexander-Spanier Normal Homology Theory of General Topological Spaces
Vladimer Baladze, Anzor Beridze, Leonard Mdzinarishvili
The Alexandroff-Čech normal cohomology theory [Mor], [Bar], [Ba],[Ba] is the unique continuous extension \cite{Wat} of the additive cohomology theory [Mil], [Ber-Mdz$_1…
On the Universal Coefficient Formula and Derived Functor
Anzor Beridze, Leonard Mdzinarishvili
It is known that homology and inverse limit functors do not commute. In the paper we consider this very problem and find its application for various homology theories. In particula…
On the Axiomatic Systems of Singular Cohomology Theory
Anzor Beridze, Leonard Mdzinarishvili
On the category of pairs of topological spaces having a homotopy type of complexes the singular (co)homology theory was axiomatically studied by J.Milnor. In particular, Milno…
On the Axiomatic Systems of Steenrod Homology Theory of Compact Spaces
Anzor Beridze, Leonard Mdzinarishvili
On the category of compact metric spaces an exact homology theory was defined and its relation to the Vietoris homology theory was studied by N. Steenrod [S]. In particular, the ho…