Oscillation Revisited
Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Beer, Gerald [verfasserIn] Cao, Jiling [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Set-valued analysis - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993, 25(2017), 3 vom: 06. Juni, Seite 603-616 |
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| Übergeordnetes Werk: |
volume:25 ; year:2017 ; number:3 ; day:06 ; month:06 ; pages:603-616 |
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| DOI / URN: |
10.1007/s11228-017-0425-8 |
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| 520 | |a Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. | ||
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10.1007/s11228-017-0425-8 doi (DE-627)SPR018005241 (SPR)s11228-017-0425-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl Beer, Gerald verfasserin aut Oscillation Revisited 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. Oscillation (dpeaa)DE-He213 Strong uniform continuity (dpeaa)DE-He213 UC-subset (dpeaa)DE-He213 Hausdorff distance (dpeaa)DE-He213 Locally finite topology (dpeaa)DE-He213 Finite topology (dpeaa)DE-He213 Strong uniform convergence (dpeaa)DE-He213 Very strong uniform convergence (dpeaa)DE-He213 Bornology (dpeaa)DE-He213 Cao, Jiling verfasserin aut Enthalten in Set-valued analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993 25(2017), 3 vom: 06. Juni, Seite 603-616 (DE-627)271348585 (DE-600)1479737-9 1572-932X nnns volume:25 year:2017 number:3 day:06 month:06 pages:603-616 https://dx.doi.org/10.1007/s11228-017-0425-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 31.40 ASE AR 25 2017 3 06 06 603-616 |
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10.1007/s11228-017-0425-8 doi (DE-627)SPR018005241 (SPR)s11228-017-0425-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl Beer, Gerald verfasserin aut Oscillation Revisited 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. Oscillation (dpeaa)DE-He213 Strong uniform continuity (dpeaa)DE-He213 UC-subset (dpeaa)DE-He213 Hausdorff distance (dpeaa)DE-He213 Locally finite topology (dpeaa)DE-He213 Finite topology (dpeaa)DE-He213 Strong uniform convergence (dpeaa)DE-He213 Very strong uniform convergence (dpeaa)DE-He213 Bornology (dpeaa)DE-He213 Cao, Jiling verfasserin aut Enthalten in Set-valued analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993 25(2017), 3 vom: 06. Juni, Seite 603-616 (DE-627)271348585 (DE-600)1479737-9 1572-932X nnns volume:25 year:2017 number:3 day:06 month:06 pages:603-616 https://dx.doi.org/10.1007/s11228-017-0425-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 31.40 ASE AR 25 2017 3 06 06 603-616 |
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10.1007/s11228-017-0425-8 doi (DE-627)SPR018005241 (SPR)s11228-017-0425-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl Beer, Gerald verfasserin aut Oscillation Revisited 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. Oscillation (dpeaa)DE-He213 Strong uniform continuity (dpeaa)DE-He213 UC-subset (dpeaa)DE-He213 Hausdorff distance (dpeaa)DE-He213 Locally finite topology (dpeaa)DE-He213 Finite topology (dpeaa)DE-He213 Strong uniform convergence (dpeaa)DE-He213 Very strong uniform convergence (dpeaa)DE-He213 Bornology (dpeaa)DE-He213 Cao, Jiling verfasserin aut Enthalten in Set-valued analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993 25(2017), 3 vom: 06. Juni, Seite 603-616 (DE-627)271348585 (DE-600)1479737-9 1572-932X nnns volume:25 year:2017 number:3 day:06 month:06 pages:603-616 https://dx.doi.org/10.1007/s11228-017-0425-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 31.40 ASE AR 25 2017 3 06 06 603-616 |
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10.1007/s11228-017-0425-8 doi (DE-627)SPR018005241 (SPR)s11228-017-0425-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl Beer, Gerald verfasserin aut Oscillation Revisited 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. Oscillation (dpeaa)DE-He213 Strong uniform continuity (dpeaa)DE-He213 UC-subset (dpeaa)DE-He213 Hausdorff distance (dpeaa)DE-He213 Locally finite topology (dpeaa)DE-He213 Finite topology (dpeaa)DE-He213 Strong uniform convergence (dpeaa)DE-He213 Very strong uniform convergence (dpeaa)DE-He213 Bornology (dpeaa)DE-He213 Cao, Jiling verfasserin aut Enthalten in Set-valued analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993 25(2017), 3 vom: 06. Juni, Seite 603-616 (DE-627)271348585 (DE-600)1479737-9 1572-932X nnns volume:25 year:2017 number:3 day:06 month:06 pages:603-616 https://dx.doi.org/10.1007/s11228-017-0425-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 31.40 ASE AR 25 2017 3 06 06 603-616 |
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10.1007/s11228-017-0425-8 doi (DE-627)SPR018005241 (SPR)s11228-017-0425-8-e DE-627 ger DE-627 rakwb eng 510 ASE 31.40 bkl Beer, Gerald verfasserin aut Oscillation Revisited 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. Oscillation (dpeaa)DE-He213 Strong uniform continuity (dpeaa)DE-He213 UC-subset (dpeaa)DE-He213 Hausdorff distance (dpeaa)DE-He213 Locally finite topology (dpeaa)DE-He213 Finite topology (dpeaa)DE-He213 Strong uniform convergence (dpeaa)DE-He213 Very strong uniform convergence (dpeaa)DE-He213 Bornology (dpeaa)DE-He213 Cao, Jiling verfasserin aut Enthalten in Set-valued analysis Dordrecht [u.a.] : Springer Science + Business Media B.V, 1993 25(2017), 3 vom: 06. Juni, Seite 603-616 (DE-627)271348585 (DE-600)1479737-9 1572-932X nnns volume:25 year:2017 number:3 day:06 month:06 pages:603-616 https://dx.doi.org/10.1007/s11228-017-0425-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 31.40 ASE AR 25 2017 3 06 06 603-616 |
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Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. |
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Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. |
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Abstract In previous joint work by G. Beer and S. Levi, the authors studied the oscillation Ω(f, A) of a function f between metric spaces 〈X, d〉 and 〈Y, ρ〉 at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f,{x}) = ω(f, x), where ω(f, x) denotes the classical notion of oscillation of f at the point x ∈ X. The main purpose of this article is to formulate a general joint continuity result for (f, A)↦Ω(f, A) valid for continuous functions. |
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