On the connectivity of graph Lipscomb's space

A central role in topological dimension theory is played by Lipscomb's space $J_{A}$ since it is a universal space for metric spaces of weight $|A|\geq \aleph _{0}$. On the one hand, Lipscomb's space is the attractor of a possibly infinite iterated function system, i.e. it is a generalized Hutchinson-Barnsley fractal. As, on the other hand, some classical fractal sets are universal spaces, one can conclude that there exists a strong connection between topological dimension theory and fractal set theory. A generalization of Lipscomb's space, using graphs, has been recently introduced (see R. Miculescu, A. Mihail, Graph Lipscomb's space is a generalized Hutchinson-Barnsley fractal, Aequat. Math., \textbf{96} (2022), 1141-1157). It is denoted by J_{A}^{\G} and it is called graph Lipscomb's space associated with the graph \G on the set $A$. It turns out that it is a topological copy of a generalized Hutchinson-Barnsley fractal. This paper provides a characterization of those graphs \G for which J_{A}^{\G} is connected. In the particular case when $A$ is finite, some supplementary characterizations are presented.Comment: 13 page

A decomposition theorem for compact groups with application to supercompactness

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact Lie group. As an application, we present a proof of an unpublished result of Charles Mills from 1978: every compact group is supercompact.Comment: 12 page

Compactness in Banach space theory - selected problems

We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m compacta

Finitely fibered Rosenthal compacta and trees

We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.Comment: Small changes, mainly in the introduction and in final remark

On realcompact topological vector spaces

[EN] This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Frechet spaces, (L F)-spaces, and their duals, (D F)-spaces and spaces of continuous real-valued functions C(X) on a completely regular Hausdorff space X. Especially (L F)-spaces and their duals arise in many fields of Functional Analysis and its applications, for example in Distributions Theory, Differential Equations and Complex Analysis. The concept of a realcompact topological space, although originally introduced and studied in General Topology, has been also studied because of very concrete applications in Linear Functional Analysis.The research for the first named author was (partially) supported by Ministry of Science and Higher Education, Poland, Grant no. 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Nitrogen metabolism in cucumber cotyledons and leaves exposed to the drought stress and excessive UV-B radiation

Plants absorb light energy for photosynthesis, and some amount of potentially damaging range of solar radiation, ultraviolet B. It accounts for less than 0.5% of the total solar radiation and the ambient current level of UV-B during the growth season provide 10 kJ·m–2 energy per day on the Earth’s surface. In the field conditions, increased UV-B radiation is often accompanied by drought, but negative effect of combined stresses is not so deleterious as the effect of one of them alone. We studied some changes in nitrogen me deficit and UV-B radiation. The stresses generally decreased the biomass and total dry matter production. Combination of water deficit and UV-B activated a stress tolerance mechanism in cucumber seedlings. The NR activity and synthesis of UV-B absorbing compounds were induced. Protection against UV-B radiation can partially involve increased production of UV-B protective pigments – slightly increased the SPAD value in cucumber cotyledons and leaves was observed. The deleterious effect of combined stresses was weaker than their additive or individual effects

Badania właściwości cieplnych materiałów ochron osobistych

Właściwości cieplne materiałów wykorzystywanych do produkcji ochron osobistych strażaków zostały wyznaczone w zakresie temperatur 25÷200°c. Badania obejmowały materiały stosowane w ubraniach specjalnych i elementach hełmu strażackiego. Ciepło właściwe materiałów zostało wyznaczone metodą skaningowej kalorymetrii różnicowej (DSC, ang. Differential Scanning Calorimetry), natomiast dyfuzyjność cieplna metodą impulsu cieplnego (LFA, ang. Laser Flash Analysis). Zbadano przykładowy zestaw tkanin pochodzący z ubrania specjalnego. Badanie dotyczyło zarówno zestawu fabrycznie nowego, jak i poddanego uprzednio obciążeniom cieplnym. Dodatkowo, wykonano symulację warunków pocenia się strażaka i porównano wyznaczone wartości efektywnego ciepła właściwego dla siedmiu różnych pakietów materiałowych w warunkach zawilgocenia oraz dla próbek suchych. Pozwoliło to na określenie wpływu rzeczywistych warunków użytkowania ubrań specjalnych na ich właściwości cieplne.Thermal properties of materials used for production of firefighters’ personal protective equipment have been determined in the temperature range of 25÷200°C. The research regarded materials used in garments and helmet. The specific heats of materials have been determined with use of Differential Scanning Calorimetry (DSC) whereas the thermal diffusivities were obtained by Laser Flash Analysis (LFA). The set of fabrics applied in protective garments offered by domestic manufacturer was tested, including factory -new clothing as well as sample previously subjected to heat load. Additionally, simulation of firefighter sweating was performed and its influence on effective specific heat values of seven different sets of fabrics was investigated. The latter measurements allowed to evaluate the influence of real service conditions on the thermal properties of protective clothing