Topological Methods in Nonlinear Analysis

Natural topologies on Colombeau algebras

Jorge Aragona, Roseli Fernandez, and Stanley O. Juriaans

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Abstract

We define intrinsic, natural and metrizable topologies ${\mathcal T}_{\Omega}, {\mathcal T}, {\mathcal T}_{s,\Omega}$ and ${\mathcal T}_s$ in ${\mathcal G}(\Omega), \overline{\mathbb K}, {\mathcal G}_s(\Omega)$ and $\overline{\mathbb K}_s$, respectively. The topology ${\mathcal T}_{\Omega}$ induces ${\mathcal T}, {\mathcal T}_{s,\Omega}$ and ${\mathcal T}_s$. The topologies ${\mathcal T}_{s,\Omega}$ and ${\mathcal T}_s$ coincide with the Scarpalezos sharp topologies.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 34, Number 1 (2009), 161-180.

Dates
First available in Project Euclid: 27 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461785690

Mathematical Reviews number (MathSciNet)
MR2581465

Zentralblatt MATH identifier
1234.46038

Citation

Aragona, Jorge; Fernandez, Roseli; Juriaans, Stanley O. Natural topologies on Colombeau algebras. Topol. Methods Nonlinear Anal. 34 (2009), no. 1, 161--180. https://projecteuclid.org/euclid.tmna/1461785690


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References

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