We propose a correspondence between the partition functions of ideal gases consisting of
both bosons and fermions and the algebraic bases of supersymmetric polynomials on the …

Building on the notion of normed category as suggested by Lawvere, we introduce notions
of Cauchy convergence and cocompleteness which differ from proposals in previous works …

Generalizing Christensen's notion of a Haar-null set and Darji's notion of a Haar-meager set,
we introduce and study the notion of a Haar-$\mathcal I $ set in a Polish group. Here …

Groups with a topology that is in consistent one way or another with the algebraic structure
are considered. Classical groups with a topology are topological, paratopological …

We study the interplay between additivity (as in the Cauchy functional equation),
subadditivity and linearity. We obtain automatic continuity results in which additive or …

The theme here is category-measure duality, in the context of a topological group. One can
often handle the (Baire) category case and the (Lebesgue, or Haar) measure cases …

We give a new theory of Beurling regular variation (Part II). This includes the previously
known theory of Beurling slow variation (Part I) to which we contribute by extending Bloom's …

A subset $ X $ of an Abelian group $ G $ is called $ midconvex $ if for every $ x, y\in X $ the
set $\frac {x+ y} 2=\{z\in G: 2z= x+ y\} $ is a subset of $ X $. We prove that a subset $ X $ of …

We extend some known results from smooth dynamical systems to the category of Lipschitz
homeomorphisms of compact metric spaces. We consider dynamical properties as robust …

Shift-compactness has recently been found to be the foundation stone of classical, as well
as topological, regular variation; most recently it has come again to prominence in new …