Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Doitchinov's Construct of Supertopological Spaces is Topological

It is shown that the construct of supertopological spaces and continuous maps is topological.

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.

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.

The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.

P-Sequential Spaces and Cleavability

∗ Supported by the Serbian Scientific Foundation, grant No 04M01

Pseudoradial Spaces: Finite Products and an Example From CH

∗ The first named author’s research was partially supported by GAUK grant no. 350, partially by the Italian CNR. Both supports are gratefully acknowledged. The second author was supported by funds of Italian Ministery of University and by funds of the University of Trieste (40% and 60%).

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.

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 54E15

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

2000 Mathematics Subject Classification: 47H10, 54E15.

A Note On Quasi-Lindelöf Spaces

Петра Г. Стайнова - Квази-линдельофовите пространства са въведени от Архангелски като усилване на слабо-линдельофовите. В тази статия се разглеждат няколко свойства на квази-линдельофовите пространства и се правят сравнения със съответни ре- зултати за линдельофовите и слабо-линдельофовите пространства. Дадени са няколко примера, включително на слабо-линдельофово пространство, което не е квази-линдельофово; на пространство, което е топологично произведение на две линдельофови, но не е дори квази-линдельофово, и на пространство, което е квази-линдельофово, но не Суслиново. Накрая са поставени няколко отворени въпроси.

Nonlinear Estimates in Anisotropic Gevrey Spaces

2002 Mathematics Subject Classification: 35G20, 47H30