Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Tychonoff's theorem for hyperspaces


Author: Frank A. Chimenti
Journal: Proc. Amer. Math. Soc. 37 (1973), 281-286
MSC: Primary 54B10; Secondary 54B20
DOI: https://doi.org/10.1090/S0002-9939-1973-0307141-1
MathSciNet review: 0307141
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ \exp ({X_i})\backslash \{ \emptyset \} $ is equipped with a topology that preserves the topological convergence of nets of sets for every $ i \in I$, then the Tychonoff product of the family $ \{ \exp ({X_i})\backslash \{ \emptyset \} :i \in I\} $ is compact if and only if $ {X_i}$ is compact for every $ i \in I$. A similar result concerning sequential compactness is valid, for countable I.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B10, 54B20

Retrieve articles in all journals with MSC: 54B10, 54B20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0307141-1
Keywords: Tychonoff product, hyperspace, compact, sequentially compact, Vietoris topology, topological convergence of sets
Article copyright: © Copyright 1973 American Mathematical Society