Hassan Al-Zoubi, Hamza Alzaareer, "Exponential Law for Mappings on Sequentially Locally Convex Topological Vector Spaces and Manifolds," WSEAS Transactions on Mathematics, vol. 25, pp. 1-5, 2026, DOI:10.37394/23206.2026.25.1
Hassan Al-Zoubi, Hamza Alzaareer. Exponential Law for Mappings on Sequentially Locally Convex Topological Vector Spaces and Manifolds.
WSEAS Transactions on Mathematics. 2026;25:1-5. 10.37394/23206.2026.25.1
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Exponential Law for Mappings on Sequentially Locally Convex Topological Vector Spaces and Manifolds
Authors: ,
Abstract: The exponential law، which is an important tool in modern topology and differential calculus,
establishes a fundamental isomorphism between function spaces over product domains and iterated mapping
spaces. This work studies this principle on the context of sequentially locally convex topological vector spaces
and manifolds with rough boundaries. We demonstrate that for a sequentially compact manifold $$N_{2}$$, the map $$Φ: C^{r,k}(N_{1} x N_{2},E) \to C^{r}(N_{1},C^{k}(N_{2},E))$$ is a homeomorphism.
Keywords:
Generalized differential calculus, Smooth compact-open topology, Infinite-dimensional manifolds, sequentially Locally convex spaces, Exponential law
Pages: 1-5 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 25, 2026, Art. #1 DOI: 10.37394/23206.2026.25.1
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