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Archimedean and geodetical biequivalences. (English) Zbl 0593.54056

The authors investigate some properties of biequivalences (see also the following review). This notion is a topological one but it is introduced in topology of AST (alternative set theory). It represents a mathematization of the phenomena of indiscernibility and of accessibility associated with each concrete observation. The property of biequivalence to be the Archimedean one is a natural generalization of the Archimedean property of real numbers. Some theorems concerning the relation of this property to other topological properties are given and also nice examples are described. A biequivalence is said to be geodetical if it can be metrized in such a manner that any two accessible points x,y may be connected by a ”segment” (linearly parametrized set such that for each triple of points the triangle equality holds). Some ”algebraical” properties of the generating sequence of a biequivalence which are equivalent with the geodetical property are described. Unfortunately no example demonstrating the usefulness of these properties is given.
Reviewer: K.Čuda

MSC:

54J05 Nonstandard topology
03E70 Nonclassical and second-order set theories
54D05 Connected and locally connected spaces (general aspects)
54E35 Metric spaces, metrizability

Citations:

Zbl 0593.54057
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