Searcharxiv⌕ Search

arXiv subjects

Alexander V. Osipov

Publications and source records attributed to Alexander V. Osipov.

69 records · Page 4Linked to original sources
arXiv2018

The Menger and projective Menger properties of function spaces with the set-open topology

For a Tychonoff space $X$ and a family $λ$ of subsets of $X$, we denote by $C_λ(X)$ the space of all real-valued continuous functions on $X$ with the set-open topology. In this paper, we study the Menger and projective Menger properties of a Hausdorff space $C_λ(X)$. Our main results state that if $λ$ is a $π$-network of $X$ then (1) $C_λ(X)$ is Menger space if and only if it is $σ$-compact, if $Y$ is a dense subset of $X$ then (2) $C_{p}(Y\vert X)$ is projective Menger space if and only if it is $σ$-pseudocompact.

math.GN↗
arXiv2018

Remarks on the Ostrovsky's Theorem

In this paper we prove that the condition one-to-one of continuous open-resolvable mapping is necessary in the Ostrovsky's Theorem. Also we get that the Ostrovsky's Problem (Is every open-LCn function between Polish spaces piecewise open for n = 2, 3, ... ?) has a negative solution for any n > 1.

math.GN↗
arXiv2017

On resolvability of Lindelöf generated spaces

In this paper we study the properties of P-generated spaces (by analogy with compactly generated). We prove that a regular Lindelöf generated space with uncountable dispersion character is resolvable. It is proved that Hausdorff hereditarily L-spaces are L-tight spaces which were defined by István Juhász, Jan van Mill in (Variations on countable tightness, arXiv:1702.03714v1). We also prove ω-resolvability of regular L-tight space with uncountable dispersion character.

math.GN↗
arXiv2017

Group structures of a function spaces with the set-open topology

In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and other algebraic structures) under the usual operations of addition and multiplication (and multiplication by scalars).

math.GN↗
arXiv2016

On sequential separability of functional spaces

In this paper, we give necessary and sufficient conditions for the space B_1(X) of first Baire class functions on a Tychonoff space X, with pointwise topology, to be (strongly) sequentially separable.

math.GN↗
arXiv2012

Uniformity of uniform convergence on the family of sets

We prove that for every Hausdorff space X and any uniform quadra space (Y,U) the topology on C(X,Y) induced by the uniformity U| of uniform convergence on the saturation family L coincides with the set-open topology on C(X,Y). In particular, for every pseudocompact space X and any metrizable topological vector space Y with uniform U the topology on C(X,Y) induced by the uniformity U| of uniform convergence coincides with the C-compact-open topology on C(X,Y), and depends only on the topology induced on Y by the uniformity U. It is also shown that in the class closed-homogeneous complete uniform spaces Y necessary condition for coincidence of topologies is Y-compactness of elements of family L.

math.GN↗
arXiv2012

The C-compact-open topology on function spaces

This paper studies the C-compact-open topology on the set C(X) of all realvalued continuous functions on a Tychonov space X and compares this topology with several well-known and lesser known topologies. We investigate the properties C-compact-open topology on the set C(X) such as submetrizable, metrizable, separable and second countability.

math.GN↗
arXiv2011

Some properties of minimal S(α) and S(α)FC spaces

A S(n)-space is S(n)-functionally compact (S(n)FC) if every continuous function onto a S(n)-space is closed. S(n)-closed, S(n)-θ-closed, minimal S(n) and S(n)FC spaces are characterized in terms of θ(n)-complete accumulation points. In paper we also give new characteristics of R-closed and regular functionally compact spaces. Results obtained to answer some questions raised by D.Dikranjan, E.Giuli, L.Friedler, M.Girou, D.Pettey and J.Porter.

math.GN↗