INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY
We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanish...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
1995-12-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31271_c4cabc4a812dd80b527cbae4f3c88738.pdf |
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| Summary: | We consider the space of weakly almost periodic functions on a
transformation semigroup (S, X , ?) and show that if X is a locally compact
noncompact uniform space, and ? is a separately continuous, separately proper,
and equicontinuous action of S on X, then every continuous function on X,
vanishing at infinity is weakly almost periodic. We also use a number of
diverse examples to show that the conditions we have imposed on the
transformation semigroup are almost essential for the inclusion to hold |
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| ISSN: | 1016-1104 2345-6914 |