On suprema of metrizable vector topologies with trivial dual. (English) Zbl 0622.46003
The following theorem is shown: Let E be an infinite dimensional separable [and locally bounded] F-space whose dual has an equicontinuous and total sequence. Then:
(a) The product topology of \(E\times E\) is the supremum of three metrizable [and locally bounded] vector topologies with trivial dual. (b) There exists on E a strictly finer metrizable [and locally bounded] separable Baire topology which is the supremum of three metrizable [and locally bounded] vector topologies with trivial dual. This theorem extends a result of N. T. Peck and H. Porta [Studia Math. 47, 63-73 (1973; Zbl 0231.46032)].
(a) The product topology of \(E\times E\) is the supremum of three metrizable [and locally bounded] vector topologies with trivial dual. (b) There exists on E a strictly finer metrizable [and locally bounded] separable Baire topology which is the supremum of three metrizable [and locally bounded] vector topologies with trivial dual. This theorem extends a result of N. T. Peck and H. Porta [Studia Math. 47, 63-73 (1973; Zbl 0231.46032)].
MSC:
| 46A04 | Locally convex Fréchet spaces and (DF)-spaces |
| 46A16 | Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) |
Keywords:
F-space; metrizable topological vector space; locally bounded space; trivial dual; Baire topologyCitations:
Zbl 0231.46032References:
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