On a problem for isometric mappings of posed by Th. M. Rassias.
On analytic models of synthetic differential geometry
On four-colourings of the rational four-space.
On Lorentz-Minkowski geometry in real inner product spaces.
On metric products
On moduli of expansion of the duality mapping of smooth Banach spaces.
On pairs of metrics invariant under a cocompact action of a group.
On some properties of the metric dimension
On the -angle and -angle in normed spaces.
On the integration theorem for Lie groupoids
On the interpoint distance sum inequality.
On the iso-taxicab trigonometry.
On the Lifshits Constant for Hyperspaces
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
On the ordered sets in -dimensional real inner product spaces.
On the plane geometry with generalized absolute value metric.
On the relation between ordered sets and Lorentz--Minkowski distances in real inner product spaces.
On the tangency of sets in generalized metric spaces for certain functions of the class
On -distance in three dimensional space.
Ordinary differential equations and their exponentials
In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.
Principal bundles, groupoids, and connections
We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.