On the product of twob R-spaces and the class 45-145-145-1of Frolík

Blasco, Jose L.

doi:10.1007/bf01897301

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E(h)(y) = H(y) Y E Y1

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1993

2023

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Cited by 3 publications

(2 citation statements)

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“…Since τ ρ induces the topology of uniform convergence on P, a standard argument by using triangle inequality shows that e P is continuous. Now, since the product of a compact space and a ρ r -space is a ρ r -space ( [26]), the evaluation map from K × X into (F USCB (R n ), H end )) is continuous. Thus, K is equicontinuous ( [22], Theorem 7.19, Theorem 7.20).…”

Section: Remarkmentioning

confidence: 99%

Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets

2023

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In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff space X into the fuzzy sets of Rn, (FUSCB(Rn),Hend), which are upper semi-continuous and have bounded support endowed with the endograph metric. Namely, we obtain positive results when X is considered to be a kr-space and C(X,(FUSCB(Rn),Hend)) is endowed with the compact open topology, as well as when we assume that X is pseudocompact and C(X,(FUSCB(Rn),Hend)) is equipped with the uniform topology.

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Section: Remarkmentioning

confidence: 99%

Endograph Metric and a Version of the Arzelà–Ascoli Theorem for Fuzzy Sets

2023

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“…In [3], Theorem 1 Blasco proved the following result: Let V be a non-empty regular closed subset of a space X. IfV is pseudocompact and does not belong to the class B, then there is a pseudocompact subspace Z of/3N and a bl~-continuous function f on X • Z which is not continuous. EXAMPLE 11.…”

Section: E(h)(y) = H(y) Y E Ymentioning

confidence: 99%