The space of locally Hölder maps from a locally compact metric space to a Banach space |
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| Author |
Department of Mechanics and Mathematics, Lviv University, Universytetska
1, Lviv, 290602, Ukraine
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| Abstract |
For a separable locally compact metric space $(X,d)$ and a
separable Banach space $Y$, $C(X,Y)$ denotes the spaces of all continuous maps
from $X$ to $Y,$ equipped with the compact-open topology. The linear subspace
$H^\mu(X,Y)\subset C(X,Y),\; \mu\in (0,1],$ consisting of all locally
$\mu\text{-Hölder}$ maps is considered. It is proved that the couple
$(C(X,Y),H^\mu(X,Y))$ is homeomorphic either to $(s,\Sigma)$ or to $(s\times
s,\Sigma\times s)$ or to $(s^\omega,\Sigma^\omega).$ Here $s=(-1,1)^\omega$ is
the pseudo-interior of the Hilbert cube and $\Sigma$ is its radial interior.
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| Keywords |
separable locally compact metric space, Banach space, continuous maps, compact-open topology, locally μ-Hölder maps
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| DOI |
doi:10.30970/ms.2.1.87-90
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Reference |
1. Bessaga C., Pe czyński A. Selected Topics in Infinite Dimensional Topology. Warszawa: PWN, 1975.
2. Sakai K. The space of Lipshchitz maps from a compactum to an absolute neighbourhood LIP extensor // Fund. Math. 1991. V.138. P.27–34. 3. Sakai K., Wong R.Y. The space of Lipshchitz maps from a compactum to a locally convex set // Top. Appl. 1989. V.32. P.223–235. 4. Engelking R. General Topology. Warszawa: PWN, 1977. 5. Banakh T. The strongly universal property in closed convex sets, preprint, 1993. Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine |
| Pages |
87-90
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| Volume |
2
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| Issue |
1
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| Year |
1993
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| Journal |
Matematychni Studii
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| Full text of paper | |
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