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pro vyhledávání: '"Bilokopytov, Eugene"'
Autor:
Bilokopytov, Eugene
We present a general result about generating group topologies by pseudo-norms. Namely, we show that if a topology has a base of sets which are closed in a certain sense, then it can be generated by a collection of pseudo-norms such that the balls in
Externí odkaz:
http://arxiv.org/abs/2410.18509
Autor:
Bilokopytov, Eugene
We carry on a more detailed investigation of the composition of locally solid convergences as introduced in [BCTvdW24], as well as the corresponding notion of idempotency considered in [Bil23]. In particular, we study the interactions between these t
Externí odkaz:
http://arxiv.org/abs/2407.17752
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an Archimedean vector lattice, order intervals are compact with respect to
Externí odkaz:
http://arxiv.org/abs/2311.15049
Autor:
Bilokopytov, Eugene
We show that for an ideal $H$ in an Archimedean vector lattice $F$ the following conditions are equivalent: $\bullet$ $H$ is a projection band; $\bullet$ Any collection of mutually disjoint vectors in $H$, which is order bounded in $F$, is order boun
Externí odkaz:
http://arxiv.org/abs/2211.11192
The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (or sublattice) of finite codimension may be written as an intersection
Externí odkaz:
http://arxiv.org/abs/2210.08805
Autor:
Bilokopytov, Eugene
We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. We show that such a convergence is defined by the convergence to $0$ on the positive cone. Some results on unbounded modification wh
Externí odkaz:
http://arxiv.org/abs/2202.02536
We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. In particular, it is shown that a sequence uo-c
Externí odkaz:
http://arxiv.org/abs/2110.08709
Autor:
Bilokopytov, Eugene
We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2104.01576
Autor:
Bilokopytov, Eugene
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some of the equivalences to the case of composition operators between vector lattices of continuous functi
Externí odkaz:
http://arxiv.org/abs/2103.08776
Autor:
Bilokopytov, Eugene
In this article we investigate the disjointly non-singular (DNS) operators. Following [8] we say that an operator $T$ from a Banach lattice $F$ into a Banach space $E$ is DNS, if no restriction of $T$ to a subspace generated by a disjoint sequence is
Externí odkaz:
http://arxiv.org/abs/2101.06566