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Not every metrizable compactum is the limit of an inverse sequence with simplicial bonding maps. (English) Zbl 1388.54011

It is well known that each compact metrizable space can be written as the inverse limit of an inverse sequence of finite polyhedra with piecewise linear bonding maps. This means that for each bonding map of the inverse system, its domain and range can be triangulated so that the bonding map is simplicial. In this short note it is shown that one can’t choose fixed triangulations on terms of the inverse system, which would make all bonding maps simplicial. To put it differently, not every metrizable compactum can be written as the inverse limit of an inverse sequence of finite triangulated polyhedra with simplicial bonding maps.
The paper was posthumously prepared and edited by Leonard R. Rubin, to whom the argument was communicated by Sibe Mardešić.
Reviewer: Ziga Virk (Litija)

MSC:

54B35 Spectra in general topology
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References:

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