The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication.
The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools.
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The compact groups having a dense infinite cyclic subgroup (known as monothetic compact groups) have been studied by many authors for their relevance and nice applications. In this paper we describe in full details the compact groups $K$ with a dense free abelian subgroup $F$ and we describe the minimum rank $r_t(K)$ of such a subgroup $F$ of $K$. Surprisingly, it is either finite or coincides with the density character $d(K)$ of $K$.}
Inspired by the fact that a compact topological group is
hereditarily normal if and only if it is metrizable, we prove that various
levels of compactness-like properties imposed on a topological group G
allow one to establish that G is hereditarily normal if and only if G is
metrizable (among these properties are locally compactness, local minimality
and \omega-boundedness). This extends recent results from  in the
case of countable compactness.
We study the Cauchy problem for 2nd order weakly hyperbolic
equations. F. Colombini, E. Jannelli and S. Spagnolo showed a
coefficient degenerating at an infinite number of points, with which the Cauchy problem is ill-posed Gevrey classes. Moreover, we olso report numerical results of the singularity detection with wavelet trasform for coefficient functions.
Our effort to weaken algebraic assumptions led us to obtain
characterizations of C(X) as Riesz spaces, real l-groups, semi-affine
lattices and real lattices by using different techniques. We present a unified
approach valid for any “convenient” category. By setting equivalent
conditions to equi-uniform continuity, we obtain a characterization of
the lattice U(Y ) in parallel with that of C(X).
Combining ideas from two of our previous papers (
and ), we refine Arhangel’skii Theorem by proving a cardinal inequality
of which this is a special case: any increasing union of strongly
discretely Lindelöf spaces without uncountable free sequences and with
countable pseudocharacter has cardinality at most continuum. We then
give a partial positive answer to a problem of Alan Dow on reflection
of cardinality by closures of discrete sets.