Descriptive Sets and the Topology of Nonseparable Banach Spaces

This paper was extensively circulated in manuscript form beginning in the Summer of 1989. It is being published here for the first time in its original form except for minor corrections, updated references and some concluding comments.

Analytic Renormings of C(K) Spaces

The aim of our present note is to show the strength of the existence of an equivalent analytic renorming of a Banach space, even compared to C∞-Fréchet smooth renormings. It was Haydon who first showed in [8] that C(K) spaces for K countable admit an equivalent C∞-Fréchet smooth norm. Later, in [7] and [9] he introduced a large clams of tree-like (uncountable) compacts K for which C(K) admits an equivalent C∞-Fréchet smooth norm. Recently, it was shown in [3] that C(K) spaces for K countable admit an equivalent analytic norm. Our Theorem 1 shows that in the class of C(K) spaces this result is the best possible.

External Characterization of I-Favorable Spaces

1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Selection of Thematic NL-knowledge from the Internet

The paper deals with methods of choice in the INTERNET of natural-language textual fragments relevant to a given theme. Relevancy is estimated on the basis of semantic analysis of sentences. Recognition of syntactic and semantic connections between words of the text is carried out by the analysis of combinations of inflections and prepositions, without use of categories and rules of traditional grammar. Choice in the INTERNET of the thematic information is organized cyclically with automatic forming of the new key at every cycle when addressing to the INTERNET.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

Embeddings of α-Modulation Spaces

2010 Mathematics Subject Classification: 42B35, 46E35.

Hausdorff Measures of Noncompactness and Interpolation Spaces

2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.

Kadec Norms on Spaces of Continuous Functions

2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.

Paracompact Spaces and Radon Spaces

We prove that if E is a subset of a Banach space whose density is of measure zero and such that (E, weak) is a paracompact space, then (E, weak) is a Radon space of type (F ) under very general conditions.

Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.

On the Range of the Fourier Transform Associated with the Spherical Mean Operator

We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

On a Stratification Defined by Real Roots of Polynomials

2000 Mathematics Subject Classification: 12D10

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.