Wyniki wyszukiwania

1

The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

100%

Okunev O.

Open Mathematics

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2013

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tom 11

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nr 10

1750-1754

EN

We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom [...] holds.

2

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

100%

Okunev O.

Open Mathematics

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2011

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tom 9

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nr 5

978-983

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.

3

LΣ(≤ ω)-spaces and spaces of continuous functions

63%

Lara I., Okunev O.

Open Mathematics

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2010

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tom 8

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nr 4

754-762

EN

We present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.

Ograniczanie wyników

3 Open Mathematics

3 Okunev O.

1 Lara I.

1 2013

1 2011

1 2010

The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

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

LΣ(≤ ω)-spaces and spaces of continuous functions