Uniform convergence for a hyperspace

Gazik, R. J.

doi:10.1090/S0002-9939-1974-0331304-3

Uniform convergence for a hyperspace
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by R. J. Gazik PDF

Proc. Amer. Math. Soc. 42 (1974), 302-306 Request permission

Abstract:

In this note a uniform convergence in the collection $C(E)$ of nonempty, compact subsets of a separated uniform convergence space E is defined. This convergence is compared with the hyperspace convergence on $C(E)$ and it is shown that the two convergences agree on Richardson’s class $\Gamma$. In the case of a regular ${T_1}$ topological space (E, t) this means that there is a uniform convergence structure on E, which induces t, such that uniform convergence in $C(E)$ is convergences in the Vietoris topology on $C(E)$.

References

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