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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Topological Structure of Non-separable Sigma-locally Compact Convex Sets

Banakh I., Banakh T., Koshino K.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 2

149--153

For an infinite cardinal K let l2 (K) be the linear hull of the standard othonormal base of the Hilbert space l2(K) of density K. We prove that a non-separable convex subset X of density K = dens(X) in a locally convex linear metric space is homeomorphic to the space.[...]

Some properties of the linear hull of the Erdoes set in [l^2]

Banach T.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 4

385-391

It is proved that the linear hull L = span E of the Erdoes set E = {(x[i]) [belongs to l^2] [...] x[i] [belongs to] Q for all i} in [l^2] has the following properties: (i) L is linearly homeomorphic to L x L, (ii) L is a countable-dimensional space, (iii) L is an F[sub sigma, delta, sigma]-set in [l^2], (iv) L is a [sigma]Z[sub n]-space for every n [is greater than or equal to] 0, (v) L is not a [sigma]Z[infinity]-space, and (vi) L is ultrabarrelled.