A generalization of the Helly theorem for functions with values in a uniform space |
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Authors: | Yu V Tret’yachenko |
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Institution: | 1.State University of Higher School of Economics in Nizhni Novgorod,Nizhni Novgorod,Russia |
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Abstract: | In this paper we consider sequences of functions that are defined on a subset of the real line and take on values in a uniform
Hausdorff space. For such sequences we obtain a sufficient condition for the existence of pointwise convergent subsequences.
We prove that this generalization of the Helly theorem includes many results of the recent research. In addition, we prove
that the sufficient condition is also necessary for uniformly convergent sequences of functions. We also obtain a representation
for regular functions whose values belong to the uniform space. |
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