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Collectionwise Hausdorffness at limit cardinals

Nobuyuki Kemoto — 1991

Fundamenta Mathematicae

The shrinking property of products of cardinals

Nobuyuki Kemoto — 1991

Fundamenta Mathematicae

The shrinking property and the B-property in ordered spaces

Nobuyuki Kemoto — 1990

Fundamenta Mathematicae

Subparacompactness in locally nice spaces

Nobuyuki Kemoto — 1989

Fundamenta Mathematicae

Countable compactness of lexicographic products of GO-spaces

Nobuyuki Kemoto — 2019

Commentationes Mathematicae Universitatis Carolinae

We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see: $\circ$ \circ ...

Separating by $G_{δ}$ -sets in finite powers of ω₁

Yasushi Hirata; Nobuyuki Kemoto — 2003

Fundamenta Mathematicae

It is known that all subspaces of ω₁² have the property that every pair of disjoint closed sets can be separated by disjoint $G_{δ}$ -sets (see [4]). It has been conjectured that all subspaces of ω₁ⁿ also have this property for each n < ω. We exhibit a subspace of ⟨α,β,γ⟩ ∈ ω₁³: α ≤ β ≤ γ which does not have this property, thus disproving the conjecture. On the other hand, we prove that all subspaces of ⟨α,β,γ⟩ ∈ ω₁³: α < β < γ have this property.

Sequential completeness of subspaces of products of two cardinals

Roman Frič; Nobuyuki Kemoto — 1999

Czechoslovak Mathematical Journal

Let $κ$ be a cardinal number with the usual order topology. We prove that all subspaces of $κ^{2}$ are weakly sequentially complete and, as a corollary, all subspaces of $ω_{1}^{2}$ are sequentially complete. Moreover we show that a subspace of ${(ω_{1} + 1)}^{2}$ need not be sequentially complete, but note that $X = A \times B$ is sequentially complete whenever $A$ and $B$ are subspaces of $κ$ .

Normal subspaces in products of two ordinals

Nobuyuki Kemoto; Tsugunori Nogura; Kerry Smith; Yukinobu Yajima — 1996

Fundamenta Mathematicae

Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of ${(λ + 1)}^{2}$ .

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Currently displaying 1 – 8 of 8

Collectionwise Hausdorffness at limit cardinals

The shrinking property of products of cardinals

The shrinking property and the B-property in ordered spaces

Subparacompactness in locally nice spaces

Countable compactness of lexicographic products of GO-spaces

Separating by $G_{δ}$ -sets in finite powers of ω₁

Sequential completeness of subspaces of products of two cardinals

Normal subspaces in products of two ordinals