Set theory and topology. An introduction to the foundations of analysis. Part I: Sets, relations, numbers

TL;DR

This paper offers a formal introduction to the foundations of analysis, covering set theory, topology, relations, order theory, and number system constructions based on ZFC axioms.

Contribution

It provides a comprehensive, formal overview of the foundational concepts in analysis, emphasizing set theory and topology from an axiomatic perspective.

Findings

Formalized theorems in general topology

Constructed number systems from set-theoretic principles

Clarified the axiomatic foundations of analysis

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.