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
-
Abstract Purpose Overcoming the flaws of current data management conditions in head and neck oncology could enable integrated informatio...
-
ACS Nano DOI: 10.1021/acsnano.6b04244 from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/2aOZU8w via...
-
JOURNAL OF JAPAN SOCIETY FOR SAFETY ENGINEERING_1998_5 from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt...
-
-
Vol.83 No.3 from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/1TkQfWM via IFTTT
-
Small size of metastatic lymph nodes with extracapsular spread greatly impacts treatment outcomes in oral squamous cell carcinoma patie...
-
Guidelines for inpatient admission after pediatric tonsillectomy have been proposed to improve the safety of this procedure. This study exam...
-
Madhavi Bhargava Journal of Family and Community Medicine 2017 24(2):131-131 from #AlexandrosSfakianakis via Alexandros G.Sfakianakis ...
Δεν υπάρχουν σχόλια:
Δημοσίευση σχολίου