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Partial orderings on real linear topological spaces

Published online by Cambridge University Press:  24 October 2008

S. Simons
S. Simons
Affiliation:
Trinity College, University of Cambridge
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Extract

The following properties of the real numbers are well known:

If (xn) is a sequence of real numbers, xn → x and xn ≥ 0 for each n then x > 0. (1)

If (xn) is a sequence of real numbers, xn → x and x > 0 then, for all sufficiently large n,xn > 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 323 - 327
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCE

(1)Bourbaki, N., Espaces vectoriels topologiques (Hermann; Paris, 1953).Google Scholar