Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

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.

On Typical Compact Convex Sets in Hilbert Spaces

Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 54E15

Kadec Norms on Spaces of Continuous Functions

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

Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.

Data Independence in the Multi-dimensional Numbered Information Spaces

The concept of data independence designates the techniques that allow data to be changed without affecting the applications that process it. The different structures of the information bases require corresponded tools for supporting data independence. A kind of information bases (the Multi-dimensional Numbered Information Spaces) are pointed in the paper. The data independence in such information bases is discussed.

Applying A Normalized Compression Metric To The Measurement Of Dialect Distance

The paper discusses the application of a similarity metric based on compression to the measurement of the distance among Bulgarian dia- lects. The similarity metric is de ned on the basis of the notion of Kolmo- gorov complexity of a le (or binary string). The application of Kolmogorov complexity in practice is not possible because its calculation over a le is an undecidable problem. Thus, the actual similarity metric is based on a real life compressor which only approximates the Kolmogorov complexity. To use the metric for distance measurement of Bulgarian dialects we rst represent the dialectological data in such a way that the metric is applicable. We propose two such representations which are compared to a baseline distance between dialects. Then we conclude the paper with an outline of our future work.

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.

Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

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.

An Example Concerning Valdivia Compact Spaces

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998