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Characterizing polyhedrons and manifolds. (English) Zbl 1097.54041
It is shown that a compact polyhedron can be axiomatized among compact spaces (or among metrizable spaces containing an arc) by first order properties of its monoid of continuous self-maps. This generalizes the result of W. Taylor [Research and Exposition in Mathematics, 13. Berlin: Heldermann Verlag (1986; Zbl 0615.54013)].
MSC:
54H99 Connections of general topology with other structures, applications
54C05 Continuous maps
54H15 Transformation groups and semigroups (topological aspects)
Citations:
Zbl 0615.54013
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