Nonmeasurable sets in tree structures and Ellentuck topology

The aim of this paper is to provide the results that answer the Kuratowski problem posed in 1935 concerning the existence of nonmeasurable sets. The Kuratowski problem was considered for partitions, here we provide a generalization to point-finite families for tree structures and structures in Ellentuck space. The main result of this paper generalizes previous results in the topic of nonmeasurable sets.Comment: arXiv admin note: text overlap with arXiv:2012.1075

Chains in Rudin-Frolik order for regulars

The aim of this paper is to construct chains of length $(2^\kappa)^+$ in the sense of Rudin-Frol\'ik order in $\beta \kappa$ for $\kappa$ regular

A note on special subsets of the Rudin-Frol\'ik order for regulars

We show that there is a set of $2^{2^{\kappa}}$ ultrafilters incomparable in Rudin-Frol\'ik order of $\beta \kappa \setminus \kappa$, where $\kappa$ is regular, for which no subset with more than one element has an infimum.Comment: arXiv admin note: substantial text overlap with arXiv:2304.00097. substantial text overlap with arXiv:2304.0139

A note on Kuratowski partitions in metric spaces

We prove that the existence of a complete metric space of cardinality at most $2^{\kappa}$ admitting Kuratowski partition is a consequence of $\kappa$ being the smallest real-valued measurable cardinal not greater than $2^{\aleph_0}$

Partitions and point-finite covers of Baire spaces

In this paper we show that the existence of Kuratowski partitions of Hausdorff Baire space is equivalent to the existence of point-finite covers of the same space

Optimization of Stand-Alone Hybrid Solar-Wind System by Using General Morphological Analysis

At the beginning of this chapter is a brief introduction to the issue of renewable energy sources. Next, aspects that should be considered when choosing a location of both solar photovoltaics panels and wind turbines are discussed. Afterwards, there is a brief theoretical introduction to the General Morphological Analysis (GMA), followed by practical application of GMA to optimize the structure of hybrid solar-wind system, which is preceded by a description of the adopted design assumptions. At the end of the chapter is a numerical model of a hybrid solar-wind system developed in the MATLAB/Simulink environment and analysis of the results of numerical simulations