Noncontinuous multifuctions

Hrycay, R.

doi:10.2140/pjm.1970.35.141

Cited by 6 publications

(4 citation statements)

References 10 publications

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“…So there is a natural extension of subcontinuity to multifunctions. The following definition is the local version of subcontinuity introduced by Hrycay [22,Definition 3.4].…”

Section: Subcontinuitymentioning

confidence: 99%

“…There is a very natural extension of subcontinuity to multifunctions, introduced by Hrycay [22] 1 . There is a large number of publications dealing with subcontinuity of either functions or multifunctions.…”

Section: Introductionmentioning

confidence: 99%

“…Subcontinuity is often treated as a supplementary property, like before mentioned "upgrade" of closed graph property into continuity. Hrycay [22] used it for investigation of connected multifunctions (multifunctions taking connected sets onto connected sets). Subcontinuity has found many applications; in [10] it is used to study closed maps, in [3] to study topological groups, in [26] to study extensions of continuous functions and in [15] to characterize minimal USCO maps.…”

Section: Introductionmentioning

confidence: 99%

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Subcontinuity

Holá

Novotný

2012

Mathematica Slovaca

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ABSTRACT. We give interesting characterizations using subcontinuity. Let X, Y be topological spaces. We study subcontinuity of multifunctions from X to Y and its relations to local compactness, local total boundedness and upper semicontinuity. If Y is regular, then F is subcontinuous iff F is USCO. A uniform space Y is complete iff for every topological space X and for every net {F a }, F a ⊂ X × Y , of multifunctions subcontinuous at x ∈ X, uniformly convergent to F , F is subcontinuous at x. A Tychonoff space Y isČech-complete (resp. G m -space) iff for every topological space X and every multifunction F ⊂ X × Y the set of points of subcontinuity of F is a G δ -subset (resp. G m -subset) of X. There is a very natural extension of subcontinuity to multifunctions, introduced by Hrycay [22]1 . There is a large number of publications dealing with subcontinuity of either functions or multifunctions. Subcontinuity is often treated as a supplementary property, like before mentioned "upgrade" of closed graph property 2010 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 54C60, 54A25, 54E15. K e y w o r d s: subcontinuous, locally totally bounded, USCO multifunction, Vietoris topology, Hausdorff uniformity,Čech complete space. Both authors were supported by VEGA 2/0047/10. 1 This is the first reference we were able to find. Probably Smithson [34] did it independently in 1975, his definition is cited more frequently.

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“…So there is a natural extension of subcontinuity to multifunctions. The following definition is the local version of subcontinuity introduced by Hrycay [22,Definition 3.4].…”

Section: Subcontinuitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Subcontinuity

Holá

Novotný

2012

Mathematica Slovaca

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“…The original definitions of subcontinuous relations [14] [23] were expressed in terms of nets in topological spaces. We shall evoke them by PROPOSITION ) and thus is finer than YJf(x).…”

Section: {Tychonoff Theorem) the Product Of Topological Spaces Is Commentioning

confidence: 99%

Compactoid and compact filters

Dolecki¹,

Greco²,

Lechicki³

1985

Pacific J. Math.

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Multivalued mappings

Borisovich¹,

Гельман²,

Obukhovskiĭ³

1984

J Math Sci

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Gel'man, Obukhovs kii UDC 517.988.52The present paper is a survey of the contemporary state of art in the theory of multivalued mappings. In it one considers different forms of continuity of multivalued mappings, one investigates differentiable and measurable multivalued mappings, one considers single-valued continuous approximations and sections of multivalued mappings, one studies fixed points of multivalued mappings and other questions of this theory. One gives references to the literature regarding applications to the theory of games, mathematical economics, the theory of differential inclusions and generalized dynamical systems. The paper contains an extensive bibliography.

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Noncontinuous multifuctions

Cited by 6 publications

References 10 publications

Subcontinuity

Subcontinuity

Compactoid and compact filters

Multivalued mappings

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