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Completion of Semiuniform Convergence Spaces

✍ Scribed by Gerhard Preuß


Book ID
110264510
Publisher
Springer
Year
2000
Tongue
English
Weight
109 KB
Volume
8
Category
Article
ISSN
0927-2852

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✍ Gerhard Preuß 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 599 KB

The importance of local precompactness has become apparent in theorems of the Ascoli type proved by Bentley and Herrlich (1985) in the realm of filter spaces as well as by Wyler (1984) in the realm of uniform limit spaces. Here local precompactness is studied in the highly convenient setting of semi

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✍ Mikael Lindsteöm 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 385 KB

## 1. Definitions and introdiiction In this note it is shown that the completion of a SCHWARTZ space E in the category of L,L, -embedded spaces is Iinearly homeomorphic with the eJf-bidual LAM E . The connection between LA,, -embedded SCHWARTZ spaces and topological SCHWARTZ spaces is also studied.