On the relationships among the axioms for a metric space and for general axiomatic systems
On the representation of orthocomplemented posets
On the rim-types of hereditarily locally connected continua
On the rotation sets for non-continuous circle maps.
On the -invariance property for -flows.
On the saturation of a topological partial algebra with respect to a congruence relation
On the Schauder fixed point theorem
The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.
On the Scott topology on the set of continuous maps
On the selector problems for the partitions of Polish spaces and for the compact-valued mappings
On the self-similar Jordan arcs admitting structure parametrization.
On the Separation Dimension of
We prove that , where trt stands for the transfinite extension of Steinke’s separation dimension. This answers a question of Chatyrko and Hattori.
On the separation properties of
On the sequential envelope
On the sequential order
On the set function
Inspired by the work that Professor Janusz R. Prajs did on homogeneous metric continua in his paper (2010) and the version of his work for Hausdorff continua with the uniform property of Effros done by this author, we introduce a new set function, , and present properties of it.
On the set of points of discontinuity for functions with closed graphs
On the set-theoretic strength of the n-compactness of generalized Cantor cubes
We investigate, in set theory without the Axiom of Choice , the set-theoretic strength of the statement Q(n): For every infinite set X, the Tychonoff product , where 2 = 0,1 has the discrete topology, is n-compact, where n = 2,3,4,5 (definitions are given in Section 1). We establish the following results: (1) For n = 3,4,5, Q(n) is, in (Zermelo-Fraenkel set theory minus ), equivalent to the Boolean Prime Ideal Theorem , whereas (2) Q(2) is strictly weaker than in set theory (Zermelo-Fraenkel set...
On the S-Euclidean minimum of an ideal class
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...
On the shape classification of manifold-like continua
On the shape of 0-dimensional paracompacta