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

• Autorzy: Banach T.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Borel set; countable-dimensional space; pre-Hilbert space; sigmaZ[sub n]-space; ultrabarrelled space; Z[sub n]-set

PL

kompleksy symplicjalne; rozmaitości; zbiór Borela

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 4
• Strony: 385--391
• Opis fizyczny: Bibliogr. 13 poz.,

Twórcy

autor

Banach T.