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The classical density topology is the topology generated by the lower density operator connected with a density point of a set. One of the possible generalizations of the concept of a density point is replacing the Lebesgue measure by the outer Lebesgue measure. It turns out that the analogous family associated with such generalized density points is not a topology. In this case, one can prove that this family is a strong generalized topology. In the paper some properties of the strong generalized topology connected with density points with respect to the outer Lebesgue measure will be presented. Moreover, among others, some characterizations of the families of meager sets and compact sets in this space will be given. [ABSTRACT FROM AUTHOR]

We concentrate on topologies generated by lower and almost-lower density operators on measurable spaces. Among others the existence of the smallest in the sense of inclusion abstract density topology on measurable space is investigated. Moreover, the separation axioms for such topologies are studied. [ABSTRACT FROM AUTHOR]

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Systematic studies of the deformation mechanisms of multilayer transition metal nitride coatings TiN/CrN, TiN/NbN, and NbN/CrN, and corresponding reference coatings of TiN, NbN, and CrN deposited by a direct current (dc) magnetron sputtering process onto silicon <100> have been performed. Mechanical characterization was conducted using a combination of microindentation and nanoindentation in the load range 30 to 150 mN and 0.5 to 3.5 mN, respectively. For both load ranges, scanning electron microscopy (SEM) in situ indentation was used to observe the indentation process including any pileup, sink-in, and fracture mechanisms specific to each coating. The coatings' microstructure, both before and after indentation, was analyzed using transmission electron microscopy (TEM). It was possible to both correlate the indentation load-displacement response to surface roughness effects and fracture modes (substrate and film cracking) and observe deformation mechanisms within the coatings. [ABSTRACT FROM AUTHOR]