The Lindelöf number of C p(X)×C p(X) for strongly zero-dimensional X

• Autorzy: Oleg Okunev
• Języki publikacji: EN

Abstrakty

EN

We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C p(X, M) is a continuous image of a closed subspace of C p(X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindelöf number of C p(X)×C p(X) coincides with the Lindelöf number of C p(X). We also prove that l(C p(X n)κ) ≤ l(C p(X)κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces.

Słowa kluczowe

EN

Topology of pointwise convergence; Lindelöf number

Kategorie tematyczne

• 54C35: Function spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 978-983

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Oleg Okunev

• Ciudad Universitaria

Bibliografia

• [1] Arhangel’skiĭ A.V., Problems in C p-theory, In: Open Problems in Topology, North-Holland, Amsterdam, 1990, 601–615
• [2] Arhangel’skiĭ A.V., Topological Function Spaces, Math. Appl. (Soviet Ser.), 78, Kluwer, Dordrecht, 1992
• [3] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
• [4] Mardešić S., On covering dimension and inverse limits of compact spaces, Illinois J. Math, 1960, 4(2), 278–291
• [5] Okunev O., On Lindelöf Σ-spaces of continuous functions in the pointwise topology, Topology Appl., 1993, 49(2), 149–166 http://dx.doi.org/10.1016/0166-8641(93)90041-B
• [6] Okunev O., Tamano K., Lindelöf powers and products of function spaces, Proc. Amer. Math. Soc., 1996, 124(9), 2905–2916 http://dx.doi.org/10.1090/S0002-9939-96-03629-5
• [7] Tkachuk V.V., Some criteria for C p(X) to be an LΣ(≤ ω)-space (in preparation)

Identyfikatory

DOI

10.2478/s11533-011-0050-y