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

100%

Okunev O.

Open Mathematics

2011

tom 9

nr 5

978-983

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.

κ-compactness, extent and the Lindelöf number in LOTS

61%

Buhagiar D., Chetcuti E., Weber H.

Open Mathematics

2014

tom 12

nr 8

1249-1264

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

Ograniczanie wyników

2 Open Mathematics

1 Buhagiar D.

1 Chetcuti E.

1 Okunev O.

1 Weber H.

1 2014

1 2011

Wyniki wyszukiwania

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

κ-compactness, extent and the Lindelöf number in LOTS