Elfard, Ali Sayed(Universitat Politècnica de València, 2015-10-01)
[EN] Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove ...
Buzyakova, Raushan Z.(Universitat Politècnica de València, 2009-10-01)
[EN] Let X be a non-paracompact subspace of a linearly ordered topological space. We prove, in particular, that if a Hausdorff topological group G contains closed copies of X and a Hausdorff compactification bX of X then ...
Buzyakova, Raushan(Universitat Politècnica de València, 2016-10-03)
[EN] We show that for any continuous monotonic bijection $f$ on a $\sigma$-compact subgroup $G\subset \mathbb R$ there exists a binary operation $+_f$ such that $\langle G, +_f\rangle$ is a topological group topologically ...
Bouziad, Ahmed(Universitat Politècnica de València, 2019-10-01)
[EN] A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is ...
Buzyakova, Raushan(Universitat Politècnica de València, 2024-04-02)
[EN] We study topological groups of monotonic automorphisms on a generalized ordered space L. We find a condition that is necessary and sufficient for the set of all monotonic automorphism on L along with the function ...
Bonanzinga, Maddalena; Cuzzupè, Maria Vittoria(Universitat Politècnica de València, 2016-04-12)
[EN] In [A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Top. Proc. 42 (2013), 157-163] it is proved that the character of a non-locally compact topological group with a first ...
Shakhmatov, Dimitri; Tkachenko, Mikhail; Tkachuk, Vladimir V.; Wilson, Richard G.(Universitat Politècnica de València, 2002-10-01)
[EN] The problem of whether a given connected Tychonoff space admits a strictly finer connected Tychonoff topology is considered. We show that every Tychonoff space X satisfying ω (X) ≤ c and c (X) ≤ N0 admits a finer ...
Fujita, Hiroshi; Shakhmatov, Dimitri(Universitat Politècnica de València, 2002-04-01)
[EN] A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood ...
Arhangelskii, A.V.; Uspenskij, Vladimir V.(Universitat Politècnica de València, 2006-04-01)
[EN] It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement ...
He, Shi-Yao; Jin, Ying-Ying; Xie, Li-Hong(Universitat Politècnica de València, 2023-10-02)
[EN] In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions ...