arXiv subjects

S. P. Gul'ko

Publications and source records attributed to S. P. Gul'ko.

4 recordsLinked to original sources

arXiv2018

Locally uniformly rotund renormings of the spaces of continuous functions on Fedorchuk compacts

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such that $f^{-1}(y)$ is metrizable for all $y\in Y$ . A continuous map of compacts $f : X \to Y$ is said to be fully closed if for any disjoint closed subsets $A;B \subset X$ the intersection $f(A) \cap f(B)$ is finite. For instance the projection of the lexicographic square onto the first factor is fully closed and all its fibers are homeomorphic to the closed interval.

math.FA↗

arXiv2018

The existence of LUR-norms on spaces of continuous functions on Fedorchuk compacta

We construct an LUR-norm on the space C(K) which is lower semicontinuous with respect to the pointwise topology for any Fedorchuk compactum of height 3.

math.FA↗

arXiv2018

Complete topological classification of Baire spaces functions on ordinals

The paper considers the spaces $B_p[1, α]$ of all Baire functions $x\colon [1,α]\to \mathbb{R}$, defined on segments of ordinals $[1,α]$ and endowed with the topology of pointwise convergence. A complete topological classification of these spaces is given

math.GN↗

arXiv2018

Classification of spaces of Continuous Function on ordinals

We conclude the classification of spaces of continuous functions on ordinals carried out by R. Gorak. This gives a complete topological classification of the spaces $C_p([0,α])$ of all continuous real-valued functions on compact segments of ordinals endowed with the topology of pointwise convergence. Moreover, this topological classification of the spaces $C_p([0,α])$ completely coincides with their uniform classification.

math.GN↗