Remarks on dense subspaces
Some constructions of spaces with/without dense subspaces satisfying stronger separation axioms are presented.
A -normal Tychonoff space which is not normal
-normality and -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff -normal non-normal space and an example of a Hausdorff -normal non-regular space.
On products of pseudoradial ѕpaces
On bases in Banach spaces
We investigate various kinds of bases in infinite-dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain complete minimal systems in as well as in separable Banach spaces.
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