The quasi-metric of complexity convergence
作者:
Salvador Romaguera,
Michel Schellekens,
期刊:
Quaestiones Mathematicae
(Taylor Available online 2000)
卷期:
Volume 23,
issue 3
页码: 359-374
ISSN:1607-3606
年代: 2000
DOI:10.2989/16073600009485983
出版商: Taylor & Francis Group
关键词: COMPLEXITY CONVERGENCE;POINTWISE CONVERGENCE;UNIFORM CONVERGENCE;QUASI-METRIC;SMYTH COMPLETE;THE GROTHENDIECK THEOREM
数据来源: Taylor
摘要:
For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences)Xω, is introduced and studied. We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity of uniform convergence. We show that it coincides with the quasi-uniformity of pointwise convergence if and only if the quasi-metric space (X, d) is bounded and it coincides with the quasi-uniformity of uniform convergence if and only ifXis a singleton. We also investigate completeness of the quasi-metric of complexity convergence. Finally, we obtain versions of the celebrated Grothendieck theorem in this context.
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