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.

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.

P-Sequential Spaces and Cleavability

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

Criterion of Normality of the Completely Regular Topology of Separate Continuity

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.

Doitchinov's Construct of Supertopological Spaces is Topological

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

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Upper and Lower Bounds in Relator Spaces

2000 Mathematics Subject Classification: 06A06, 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.