Quasi-Suslin weak duals
نویسندگان
چکیده
منابع مشابه
The incompleteness of weak duals
1. Incompleteness of weak duals of reasonable spaces 2. Appendix: locally-convex limits and colimits 3. Appendix: ubiquity of quasi-completeness The point here is to prove that the weak duals of reasonable topological vector spaces, such as infinite-dimensional Hilbert, Banach, or Fréchet spaces, are not complete. That is, in these weak duals there are Cauchy nets which do not converge. Happily...
متن کاملDuals of quasi-3 designs are not necessarily quasi-3
In the early 1980s Dan Hughes wrote two papers on semi-symmetric 3-designs, which are closely related to quasi-3 designs. In 1973 Peter Cameron asked whether the dual design of any quasi-3 design must also be quasi-3. In this article we answer that question. We give some general constructions of quasi-3 designs which enable us to give the answer. The answer is no.
متن کاملSuslin Lattices
In their work on spreading models in Banach spaces, Dilworth, Odell, and Sari [4] introduced the notion of a Suslin lower semi-lattice, a seemingly slight weakening of the notion of a Suslin tree. They posed several problems of a set theoretic nature regarding their notion. In this paper, we make a systematic study of the notion of Suslin lower semi-lattice, answering some of the questions rais...
متن کاملSuslin Sets
Proof. Suppose z is in the RHS. Then, for some f ∈ Y X , z ∈ Sxfx for all x ∈ X. Hence for each x ∈ X there is y = fx so that z ∈ Sxy, so z is in the LHS. Suppose z is in the LHS. Then for each x ∈ X there is some y ∈ Y so that z ∈ Sxy. Hence for each x ∈ X the set Tx = { y : z ∈ Sxy } is not empty. By AC there is a function f ∈ Y x so that, for all x ∈ X, fx ∈ Tx. Hence, for all x ∈ X, z ∈ Sxf...
متن کاملThe weak topology of locally convex spaces and the weak-* topology of their duals
These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.07.081