Study of families of monotone continuous functions on Tychonoff spaces

Okhezin, D. S.

doi:10.1007/s10958-007-0259-2

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Teorema De Representación De Goetschel Y Voxman1

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2012

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Cited by 2 publications

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“…El teorema anterior relaciona el estudio de los números difusos con el estudio de funciones monótonas. En este contexto, pueden ser de interés las técnicas desarrolladas en [28,62].…”

Section: Teorema De Representación De Goetschel Y Voxmanunclassified

Espacios de funciones continuas con valores difusos

Mínguez¹

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“…El teorema anterior relaciona el estudio de los números difusos con el estudio de funciones monótonas. En este contexto, pueden ser de interés las técnicas desarrolladas en [28,62].…”

Section: Teorema De Representación De Goetschel Y Voxmanunclassified

Espacios de funciones continuas con valores difusos

Mínguez¹

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On the Fuzzy Number Space with the Level Convergence Topology

Font

Miralles

Sanchis

2012

Journal of Function Spaces and Applications

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We characterize compact sets of E 1 endowed with the level convergence topology τ . We also describe the completion E 1 , U of E 1 with respect to its natural uniformity, that is, the pointwise uniformity U, and show other topological properties of E 1 , as separability. We apply these results to give an Arzela-Ascoli theorem for the space of E 1 , τ -valued continuous functions on a locally compact topological space equipped with the compact-open topology.The fuzzy number space E 1 is the set of elements u of F R satisfying the following properties:1 u is normal, that is, there exists an x 0 ∈ R with u x 0 1;2 u is convex, that is, u λx 1 − λ y ≥ min{u x , u y } for all x, y ∈ R, λ ∈ 0, 1 ; 2 Journal of Function Spaces and Applications 3 u is upper-semicontinuous; 4 u 0 is a compact set in R.The λ-level set u λ of u ∈ E 1 is a compact interval for each λ ∈ 0, 1 . We denote u λ u − λ , u λ . Notice that every r ∈ R can be considered a fuzzy number since r can be identified with the fuzzy number r defined as r t : 1 if t r, 0 if t / r.

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Study of families of monotone continuous functions on Tychonoff spaces

Cited by 2 publications

References 7 publications

Espacios de funciones continuas con valores difusos

Espacios de funciones continuas con valores difusos

On the Fuzzy Number Space with the Level Convergence Topology

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