Abstract

definitions and explanations frequently come together and permeate almost all fields of knowledge. This does not exclude mathematics, even when these definitions hold clear links and close connections with our physical world. Here we propose a rather different perspective. Making operational physical assumptions, we show how it is possible to rigorously reconstruct some features of both geometry and topology. Broadly speaking, assuming this operational and more concrete philosophy we not only are capable of defining primitive concepts like points, straight lines, planes, angles and spaces, but we also go all the way up to more complex constructions. We show that within our method it is also possible to come up with what we call a compass-based topology as well as a normed and a metric space. We hope this operationalist point-of-view can assist other researchers and students to have a clearer understanding of these quite abstract concepts.