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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 .

Normal Vietoris implies compactness: a short proof

G. Di Maio, E. Meccariello, Somashekhar Naimpally (2004)

Czechoslovak Mathematical Journal

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.

Note on countable unions of Corson countably compact spaces

Ondřej F. K. Kalenda (2004)

Commentationes Mathematicae Universitatis Carolinae

We show that a compact space K has a dense set of G δ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in K , then K is even Corson.

Notes on monotone Lindelöf property

Ai-Jun Xu, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.

Notes on strongly Whyburn spaces

Masami Sakai (2016)

Commentationes Mathematicae Universitatis Carolinae

We introduce the notion of a strongly Whyburn space, and show that a space X is strongly Whyburn if and only if X × ( ω + 1 ) is Whyburn. We also show that if X × Y is Whyburn for any Whyburn space Y , then X is discrete.

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