Ideals of uniformly continuous mappings on pseudometric spaces
In search for Lindelöf ’s
It is shown that if is a first-countable countably compact subspace of ordinals then is Lindelöf. This result is used to construct an example of a countably compact space such that the extent of is less than the Lindelöf number of . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.
Indicatrix of Banach and a Space of Continuous Functions
Intégrité du complété et théorème de Stone-Weierstrass
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...
Iterated and double limits