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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 1999

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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.

Refining two Marciszewski's constructions related to the Sierpiński-Kuratowski technique

Nunez Garcia J.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 2

157-161

Refining two Marciszewski's constructions, we present an example of a line-free group with no continuous functions onto its own square, and we give a new proof showing that van Mill's space L [6] is not homeomorphic to L x Z for any nontrival Z.