Commentary on Menger’s “Untersuchungen über allgemeine Metrik”

Peter Plaumann and Karl Strambach

A chapter in Selecta Mathematica, 2002, pp 229-233 from Springer

Abstract: Abstract The original models for topological spaces were subsets of the real line and its Cartesian powers, i.e., metric spaces. However, in the early years of the twentieth century, the founders of point-set topology strove to base that subject on concepts that were independent of any particular metric space notions and to expand the domain of validity of known metric space results to this more general setting. They also placed topological invariants into the foreground. It soon became apparent that many metric-space results retained their validity, but at a price — namely, the loss of geometric intuition and visualization; for example, there is no topological distinction between metric Spaces with equivalent metrics.

Date: 2002
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DOI: 10.1007/978-3-7091-6110-4_19

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