In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

Generalized Haar wavelets were introduced in connection with the problem of detecting specific periodic components in noisy signals. John Benedetto and I showed that the non–normalized continuous wavelet transform of a periodic function taken with respect to a generalized Haar wavelet is periodic in time as well as in scale, and that generalized Haar wavelets are the only bounded functions with...

In this paper, variety means a class of similar algebras—i.e., models of one firstorder language without relation symbols—which is defined by the satisfaction of some fixed sets of equations. A variety is locally finite if all of its finitely generated members are finite. Following J. Berman and P. Idziak [2], the G-spectrum, or generative complexity, of a locally finite variety C, is the funct...

For a Jordan domain with smooth boundary, the boundary rotation h is defined as the total variation of the direction angle of the tangent to the boundary curve under a complete circuit. The domain is said to have bounded turning or rotation if h < 1 and the functions under such mappings are called functions of bounded boundary turning or rotation. We define a generalization of this concept and ...

Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topolo...

A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct. The lid-chromatic number of a graph is the minimum number of colors used by a locally identifying vertex-coloring. In this paper, we prove that for any graph class of bounded expansion, the lid-chromatic number is bounded. Cla...

We present problems in different application areas: tandem repeats (computational biology), poetry and music analysis, and author validation, that require a more sophisticated pattern matching model that hitherto considered. We introduce a new matching criterion—generalized function matching—that encapsulates the notion suggested by the above problems. The generalized function matching problem ...

Our paper is devoted to two classical problems of category theory: the Orthogonal Subcategory Problem which asks, given a class H of morphisms, whether the subcategory H⊥ of all objects orthogonal to every member of H is reflective. And the Small Object Argument which asks whether the subcategory InjH of all objects injective to every member of H is weakly reflective and, moreover, the weak ref...