Relations With I-structure in Categories With Pullbacks
Relativnullen und reduzible Mengen bei Differenzen von Mengen ganzer Zahlen.
Resultats sur la comparaison des types d΄ordres
Some combinatorial problems, connected with product-isomorphisms of binary relations
Some complexity results in topology and analysis
If X is a compact metric space of dimension n, then K(X), the n- dimensional kernel of X, is the union of all n-dimensional Cantor manifolds in X. Aleksandrov raised the problem of what the descriptive complexity of K(X) could be. A straightforward analysis shows that if X is an n-dimensional complete separable metric space, then K(X) is a or PCA set. We show (a) there is an n-dimensional continuum X in for which K(X) is a complete set. In particular, ; K(X) is coanalytic but is not an analytic...
Some Remarks on Reproductive Solutions
Some topological properties of -covering sets
We prove the following theorems: There exists an -covering with the property . Under there exists such that is not an -covering or is not an -covering]. Also we characterize the property of being an -covering.
Strong measure zero and meager-additive sets through the prism of fractal measures
We develop a theory of sharp measure zero sets that parallels Borel’s strong measure zero, and prove a theorem analogous to Galvin–Mycielski–Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of is meager-additive if and only if it is -additive; if is continuous and is meager-additive, then so is .
Sur quelques classes universelles de relations -aires
The algebraic uniqueness of the addition of natural numbers.
The ideal (a) is not generated
We prove that the ideal (a) defined by the density topology is not generated. This answers a question of Z. Grande and E. Strońska.
The maximal regular ideal of the semigroup of binary relations
The structure of an idempotent relation.
Theorems on sets not belonging to algebras.
Three problems of S. M. Ulam with solutions and generalizations
Transitive closures of binary relations. I.
Transitive closures of binary relations II.
Transitive closures of binary relations. III.
Transitive closures of binary relations. IV.