The codensity character of topological vector spaces. (English) Zbl 0888.46002
Lau, Anthony To-Ming (ed.) et al., Topological vector spaces, algebras and related areas. Proceedings of the international conference, held at McMaster University, Hamilton, Canada during May 2-6, 1994 in honor of Dr. Taqdir Husain on the occasion of his retirement. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 316, 24-36 (1994).
The codensity character, i.e. the supremum of codimensions of dense subspaces in a given topological vector space is investigated. The range of possibilities for value of codensity character is demonstrated. Some sufficient conditions for a space \(E\) to be fit are provided. (\(E\) is called fit if its codensity character is a maximum equal to dimension of \(E\).) A necessary condition is that there is a fully discontinuous Hamel basis for \(E\). It is shown that the existence of fully discontinuous basis does not imply fitness in general. (The equivalence [\(E\) is fit]\(\Leftrightarrow\)[\(E\) has fully discontinuous basis] is proved under certain circumstances in a subsequent study.) The results of the paper are also relevant for the BCE problem.
For the entire collection see [Zbl 0817.00016].
For the entire collection see [Zbl 0817.00016].
Reviewer: J.Hamhalter (Praha)
MSC:
| 46A35 | Summability and bases in topological vector spaces |
| 46A03 | General theory of locally convex spaces |
