Multifunctions and graphs

Joseph, James E.

doi:10.2140/pjm.1978.79.509

Cited by 18 publications

(14 citation statements)

References 12 publications

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“…Remark 5.13. In [8], Joseph defined the concept of subclosed graphs for multifunctions as a generalization of closed graphs and showed that if a multifunction F : X ->Y has a subclosed graph and if is a compact subset of Y then F~(K) is closed in X [8,Theorem 3.15]. Therefore, the condition "closed" on G(F) in Theorem 5.12 can be replaced by "subclosed".…”

Section: Therefore F+(v) = F + (Y -Fr(v)) D Pint(f+(cl(f))) E Po(x) mentioning

confidence: 99%

Almost Weakly Continuous Multifunction

Noiri¹,

Popa²

1993

Demonstratio Mathematica

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Section: Therefore F+(v) = F + (Y -Fr(v)) D Pint(f+(cl(f))) E Po(x) mentioning

confidence: 99%

Almost Weakly Continuous Multifunction

Noiri¹,

Popa²

1993

Demonstratio Mathematica

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“…It seems to be one of the earliest systematic and general studies of the subject; later followed by others, e.g., [45,65].…”

Section: Introductionmentioning

confidence: 99%

Invariant sets and Knaster-Tarski principle

Leśniak

2012

Open Mathematics

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“…(This is an analogy to the relation of subcontinuity of a function and its continuity, which was one of the motivations of definition of subcontinuity.) Basic references to this part are [25], [23], [34]. There are also summarized some relations among subcontinuity, local compactness and local total boundedness, which are generalizations of the work of Mimna and Wingler [29] and our previous work [31].…”

Section: Introductionmentioning

confidence: 99%

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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Multifunctions and graphs

Cited by 18 publications

References 12 publications

Almost Weakly Continuous Multifunction

Almost Weakly Continuous Multifunction

Invariant sets and Knaster-Tarski principle

Subcontinuity

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