P-adic Measures and P-adic Spaces of Continuous Functions
Abstract
For
a Hausdorff zero-dimensional topological space and
a Hausdorff non-Archimedean locally convex space, let
(resp.
) be the space of all continuous (resp. bounded continuous )
-valued functions on
. Some of the properties of the spaces
, equipped with certain locally convex topologies, are studied. Also, some complete spaces of measures, on the algebra of all clopen subsets of
, are investigated.
![X](http://212.189.136.205/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![E](http://212.189.136.205/plugins/generic/latexRender/cache/3a3ea00cfc35332cedf6e5e9a32e94da.png)
![C(X,E)](http://212.189.136.205/plugins/generic/latexRender/cache/a32eba4b78bbd50b1114233669e352f9.png)
![C_{b}(X,E)](http://212.189.136.205/plugins/generic/latexRender/cache/38adce1664ac9c92acbaac87e6425b42.png)
![E](http://212.189.136.205/plugins/generic/latexRender/cache/3a3ea00cfc35332cedf6e5e9a32e94da.png)
![X](http://212.189.136.205/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![C(X,E),\ \ C_{b}(X,E)](http://212.189.136.205/plugins/generic/latexRender/cache/ca3e836aff67f7e31fe1b8623671b5b9.png)
![X](http://212.189.136.205/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
DOI Code:
10.1285/i15900932v30n1p61
Keywords:
Non-Archimedean fields; zero-dimensional spaces; Banaschewski compactification; locally convex spaces
Non-Archimedean fields; zero-dimensional spaces; Banaschewski compactification; locally convex spaces
Classification:
46S10; 46G10
Full Text: PDF