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Two theorems on generalised metric spaces

Published online by Cambridge University Press:  17 April 2009

Sergey Svetlichny
Sergey Svetlichny
Affiliation:
School of Computing and Mathematics, Deakin University, Clayton Vic 3168, Australia e-mail: svet@deakin.edu.au
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We prove that any compact space, and even any countably compact space having the weak topology with respect to a sequence of symmetrisable subspaces, is metrisable. This generalises results of Arhangel'skii and Nedev on metrisability of symmetrisable compact spaces. Also we define and study contraction functions on generalised metric spaces whose topology can be described in terms of a ‘distance function’ which is not quite a metric. In particular we present necessary and sufficient conditions for a space of countable pseudo-character to be submetrisable in terms of real-valued contraction functions on this space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 197 - 206
Copyright
Copyright © Australian Mathematical Society 1997

References

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