By P. K. Kamthan
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13, p. 200. c. TVS (X,T). ß (X*,X)-separable, then Y* is ß (Y*,Y)-separable. c. TVS such that each X? is ß(X^,X^)-separable, then the dual X* of X = n^>1 X^ is ß (X*,X)-separable. 22 Chap. 20 Let
C. TVS (X,T). ß (X*,X)-separable, then Y* is ß (Y*,Y)-separable. c. TVS such that each X? is ß(X^,X^)-separable, then the dual X* of X = n^>1 X^ is ß (X*,X)-separable. 22 Chap. 20 Let
A rizable, t is generated by one such F-norm. 14 ology on X. (i) (ii) If т is met- Let (X,t ) be an F-space and let p ^ т be a linear top Then If the net x 0 in p but /->0 in t , then there are linear a topologies A and у on X such that (a) p с Л с у с т; (b) у is т metrizable and Л-polar; (с) x^ ^ 0 in A but x^ 0 in y. If u is in B but is not in B , then there are linear topolop gies A and у satisfying (a), (b) above and (c) ' u € but T Sec. 9 Reflexive and Montel Spaces (iii) 25 U * 8XIf T is locally bounded, then there is a linear topology у with у с T, and т is y-polar.