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In this paper we introduce a new class of rag-continuous mapping and studied some of its basic properties. We obtain some characterizations of such fuctions. Moreover we define subminimal structure and further study certain properties of rag-closed sets. [ABSTRACT FROM AUTHOR]

We show the relevance of multifractal analysis for some problems in image processing. We relate it to the standard question of the determination of correct function space settings. We show why a scale-invariant analysis, such as the one provided by wavelets, is pertinent for this purpose. Since a good setting for images is provided by spaces of measures, we give some insight into the problem of multifractal analysis of measures using wavelet techniques. [ABSTRACT FROM AUTHOR]

Chapter 5.9 of the book "Topology and Groupoids" is presented. It discusses the problem of finding a suitable topology for spaces of continuous functions with large number of literatures on general topology. It implies that the general case of the problem has proved not entirely tractable within the traditional outlook of general topology through the use of topological spaces and continuous functions.

Chapter 4.5 of the book "Topology and Groupoids" is presented. It explores the special kind of identification space and adjunction space which are commonly found in the useful theorems. It highlights the type of universal property which occurs in a diverse situation. It also shows on how to construct spaces using the adjunction spaces and at the same time help to grasp the topology of a given space.

Chapter 2.10 of the book "Topology and Groupoids" is presented. It discusses that a topological space X is Hausdorff if distinct points of X have disjoint neighbourhoods. It offers some exercises that sketch the construction of two important classes of non-Hausdorff spaces such as the Zariski topology and the sheaf of germs of functions.

Besides bounded mappings from a Sobolev space to its dual, there is an alternative understanding of differential operators as unbounded operators from a (typically dense) subset of a function space to itself. This calls for a generalization of a monotonicity concept for mappings D → X, with X a Banach space and D its subset. Moreover, X need not be reflexive because the weak-compactness arguments will be replaced by metric properties and completeness. The main benefit from this approach will be achieved for evolution problems in Chapter 9 but the method is of some interest in steady-state problems themselves. [ABSTRACT FROM AUTHOR]

The encyclopedia entry for the term Lipschitz is presented. It refers to a function that is said to be where every pair of points are less than or equal to other values.