Topology and Foundations

Dear Colleagues,

A foundational example in topology leading to graph theory as a new branch of mathematics is when Leonhard Euler demonstrated that it was impossible to find a route through the town of Königsberg (now Kaliningrad) that would cross each of its seven bridges exactly once (with the result depending only on connectivity properties—which bridges connect to which islands or riverbanks).

Subjects included in topology are graph theory and algebraic topology. Topology is foundational in number theory, algebraic geometry, category theory and homological algebra, K-theory, group theory and generalizations, topological groups and Lie groups, dynamical systems and ergodic theory, functional analysis, quantum theory, game theory, etc. Topology is in all fields of engineering, physical sciences, life sciences, social sciences, medicine and even arts, economics, finance, and finally mathematics-related sciences: informatics, physics, chemistry and biology.

Foundations extend beyond topology as the basis or groundwork of anything. Foundations are under algebraic geometry, tropical geometry, logic and deductive systems, functions, algebraic topology, homotopy theory, probability theory, stochastic processes, statistics, physics (fluid mechanics, optics, electromagnetic theory, thermodynamics, heat transfer, equilibrium and time-dependent statistical mechanics) and finally quantum information and its processing.

The aim of this Topical Collection is to bring together recent scientific advances, reviews, communications and short notes dealing with topology and foundations.

Prof. Dr. Lorentz Jäntschi
Prof. Dr. Dušanka Janežič
Collection Editors

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