| 29 May 2013 |
Set theory and topology. An introduction to the foundations
of analysis. Part I: Sets, relations, numbers
pdf
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Abstract
We provide a formal introduction into the classic theorems of
general topology and its axiomatic foundations in set theory.
Starting from ZFC, the exposition in this first part includes
relation and order theory as well as a construction of number
systems.
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| 29 May 2013 |
Set theory and topology. An introduction to the foundations
of analysis. Part II: Topology – Fundamental notions
pdf
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Abstract
We provide a formal introduction into the classic theorems of
general topology and its axiomatic foundations in set theory.
In this second part we introduce the fundamental concepts of
topological spaces, convergence, and continuity, as well as
their applications to real numbers. Various methods to
construct topological spaces are presented.
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