If and are Tychonoff spaces, let and be the free locally convex space over and , respectively. For general and , the question of whether can be embedded as a topological vector subspace of is difficult. The best results in the literature are that if can be embedded as a topological vector subspace of , where , then is a countable-dimensional compact metrizable space. Further, if is a finite-dimensional compact metrizable space, then can be embedded as a topological vector subspace of . In this paper, it is proved that can be embedded in as a topological vector subspace if is a disjoint union of a countable number of finite-dimensional locally compact separable metrizable spaces. This is the case if It is also shown that if and denote the Cantor space and the Hilbert cube , respectively, then (i) is embedded in if and only if is a zero-dimensional metrizable compact space; (ii) is embedded in if and only if is a metrizable compact space.
from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/2Gb772U
via IFTTT
Εγγραφή σε:
Σχόλια ανάρτησης (Atom)
Δημοφιλείς αναρτήσεις
-
Publication date: Available online 4 January 2018 Source: European Journal of Radiology Author(s): Peiyao Zhang, Jing Wang, Qin Xu, Zhen...
-
Dtsch med Wochenschr DOI: 10.1055/s-0043-100054 Hintergrund und Fragestellung Ein etablierter Weg, die optimale Behandlung von Tumorpatien...
-
Publication date: March 2017 Source: Free Radical Biology and Medicine, Volume 104 from #AlexandrosSfakianakis via Alexandros G.Sfak...
-
Background Hyperthyroidism is associated with increased thrombotic risk. As contact system activation through formation of neutrophil extrac...
-
Antibodies, Vol. 9, Pages 21: Construction of Ant... In Vivo and In Vitro Evaluation of Bull Semen Pro... Vertebral artery fenestration mimi...
-
Deepak Thapa, Vanita Ahuja, Deepanshu Dhiman Indian Journal of Anaesthesia 2017 61(12):1012-1014 from #AlexandrosSfakianakis via Alexa...
-
Editors' Recognition for Reviewing in 2020 No abstract available Establishing Satellite Lung Cancer Screening Sites With Telehealth to A...
-
ecancer is supporting #BowelCancerAwarenessMonth https://t.co/opXxCAAxzE from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inore...
-
Abstract Silvicultural models are often developed and applied without due consideration of fire modelling. Yet, this information is import...
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου