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A note on the extent of two subclasses of star countable spaces

100%

Yu Z.

Open Mathematics

2012

tom 10

nr 3

1067-1070

We prove that every Tychonoff strongly monotonically monolithic star countable space is Lindelöf, which solves a question posed by O.T. Alas et al. We also use this result to generalize a metrization theorem for strongly monotonically monolithic spaces. At the end of this paper, we study the extent of star countable spaces with k-in-countable bases, k ∈ ℤ.

Remarks on absolutely star countable spaces

88%

Song Y.-K.

Open Mathematics

2013

tom 11

nr 10

1755-1762

We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming $$2^{\aleph _0 } = 2^{\aleph _1 }$$, there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).

Ograniczanie wyników

2 Open Mathematics

1 Song Y.-K.

1 Yu Z.

1 2013

1 2012

Wyniki wyszukiwania

A note on the extent of two subclasses of star countable spaces

Remarks on absolutely star countable spaces