Nonstandard analysis is a way of doing calculus and analysis with infinitesimals. The historical approach of Leibniz, Euler, and others to infinitesimal calculus was gradually replaced by epsilon, delta techniques in the context of a real continuum, in the 19th century. It was not until the 1960s ...

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34
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Which topological spaces admit a nonstandard metric?

My question is about the concept of nonstandard metric space that would arise from a use of the nonstandard reals R* in place of the usual R-valued metric. That is, let us define that a topological ...
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Isomorphism types or structure theory for nonstandard analysis

My question is about nonstandard analysis, and the diverse possibilities for the choice of the nonstandard model R*. Although one hears talk of the nonstandard reals R*, there are of course many ...