We introduce a concept of Cauchy complete Császár frames and construct Cauchy completions of Császár frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

The unfolding of (1-)safe Petri nets to occurrence nets is well understood. There is a universal characterization of the unfolding of a safe net which is part and parcel of a coreflection from the category of occurrence nets to the category of safe nets. The unfolding of general Petri nets, nets with multiplicities on arcs whose markings are multisets of places, does not possess a directly anal...

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y , where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.

Bornological universes were introduced by Hu in [11] and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. In [11] and [12] Hu gives a necessary and sufficient condition for which a bornological universe is metrizable. In this article we will give a characterization of uniformizable bornological universes. Furthermore, a cons...