Zobrazeno 1 - 10
of 194
pro vyhledávání: '"Osipov, Alexander P"'
Autor:
Osipov, Alexander V.
A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the characterizat
Externí odkaz:
http://arxiv.org/abs/2409.02913
Autor:
Osipov, Alexander V.
A space $X$ is sequentially separable if there is a countable $S\subset X$ such that every point of $X$ is the limit of a sequence of points from $S$. In 2004, N.V. Velichko defined and investigated concepts close to sequentially separability: $\sigm
Externí odkaz:
http://arxiv.org/abs/2406.03014
Autor:
Lipin, Anton E., Osipov, Alexander V.
We prove that for every normal topological space $X$ and any function $f: X \to \mathbb{R}$ there is a continuous function $g : X \to \mathbb{R}$ such that $$|f(x) - g(x)| \leq \frac{1}{2} \sup\limits_{p \in X} \inf\limits_{O(p)} \sup\limits_{a,b \in
Externí odkaz:
http://arxiv.org/abs/2403.04004
A space is called Dieudonn\'{e} complete if it is complete relative to the maximal uniform structure compatible with its topology. In this paper, we investigated when the function space $C(X,Y)$ of all continuous functions from a topological space $X
Externí odkaz:
http://arxiv.org/abs/2401.15923
Autor:
Osipov, Alexander V.
A topological space $X$ is called almost discrete, if it has precisely one nonisolated point. In this paper, we get that for a countable product $X=\prod X_i$ of almost discrete spaces $X_i$ the space $C_p(X)$ of continuous real-valued functions with
Externí odkaz:
http://arxiv.org/abs/2312.10724
Autor:
Osipov, Alexander V.
In this paper we get characterizations countable tightness, countable fan-tightness and countable strong fan-tightness of spaces of quasicontinuous functions with the topology of pointwise convergence from a open Whyburn $T_2$-space $X$ into the disc
Externí odkaz:
http://arxiv.org/abs/2311.07517
In this paper we study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson's results to some class of pseudocompact spaces. Also, we introduce a concept of a weak $q
Externí odkaz:
http://arxiv.org/abs/2309.11347
In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform convergenc
Externí odkaz:
http://arxiv.org/abs/2305.04968
Autor:
Bhardwaj, Manoj, Osipov, Alexander V.
In this paper, we proved that a clopen version $S_1(C_O, C_O)$ of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space $(X, d)$, $X$ satisfies $S_1(C_O, C_O)$ if, and only if, $X$ has Borel st
Externí odkaz:
http://arxiv.org/abs/2303.06487
Autor:
Bhardwaj, Manoj, Osipov, Alexander V.
In this paper, we prove the following Theorems 1. An extremally disconnected space $X$ has the semi-Menger property if and only if One does not have a winning strategy in the game $G_{fin}(sO,sO)$. 2. An extremally disconnected space $X$ has the semi
Externí odkaz:
http://arxiv.org/abs/2303.05196