75 citations · 114 across the 41 of their papers we have counts for
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Thomassen's proof and Filippov's proof of the Weak Jordan Theorem
Martin Klazar
We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnecte…
Catalan's conjecture is Mihăilescu's theorem
Martin Klazar
This text evolves from the lecture notes for my course on Catalan's conjecture in winter term 2025/26. The ultimate goal is to give full details of Mihăilescu's proof. Current chap…
Elementary Real Analysis
Martin Klazar
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Five numeric domains; 2. Limits of real sequences; 3. Series; 4. Limits of real fun…
The Newton integral and the Stirling formula
Martin Klazar
We present details of logically simplest integral sufficient for deducing the Stirling asymptotic formula for n!. It is the Newton integral, defined as the difference of values of…
Real numbers as infinite decimals and irrationality of
Martin Klazar
In order to prove irrationality of \sqrt{2} by using only decimal expansions (and not fractions), we develop in detail a model of real numbers based on infinite decimals and arithm…