Displaying similar documents to “Some remarks on the product of two C α -compact subsets”

On locales whose countably compact sublocales have compact closure

Themba Dube (2023)

Mathematica Bohemica

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Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called cl -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.

Support vector machine skin lesion classification in Clifford algebra subspaces

Mutlu Akar, Nikolay Metodiev Sirakov (2019)

Applications of Mathematics

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The present study develops the Clifford algebra Cl 5 , 0 within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the Cl 5 , 0 we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D...

ω H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

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A subset A of a Hausdorff space X is called an ω H-set in X if for every open family 𝒰 in X such that A ⊂ ⋃ 𝒰 there exists a countable subfamily 𝒱 of 𝒰 such that A ⊂ ⋃ { V ¯ : V ∈ 𝒱 } . In this paper we introduce a new cardinal function t s θ and show that | A | ≤ 2 t s θ ( X ) ψ c ( X ) for every ω H-set A of a Hausdorff space X .

Compacta are maximally G δ -resolvable

István Juhász, Zoltán Szentmiklóssy (2013)

Commentationes Mathematicae Universitatis Carolinae

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It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum X contains Δ ( X ) many pairwise disjoint dense subsets, where Δ ( X ) denotes the minimum size of a non-empty open set in X . The aim of this note is to prove the following analogous result: Every compactum X contains Δ δ ( X ) many pairwise disjoint G δ -dense subsets, where Δ δ ( X ) denotes the minimum size of a non-empty G δ set in X .