ABSTRACT
We carried out a topological study of 72 chemical elements taking advantage of chemometric tools and general topology. We defined every element as an ordered set of 128 properties (physico-chemical and chemical), then applied PCA and cluster analysis CA (4 similarity measures and 5 grouping methodologies). Afterwards we took dendrograms (complete binary trees) of the CA and developed a mathematical methodology to extract neighbourhood relationships of those trees. By means of this approach we builded up a basis for a topology on the set of chemical elements and then provided with a topology the same set. Finally we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements such as alkaline metals, alkaline earths, noble gases, metals and non-metals. We found that alkaline metals, alkaline earths and noble gases appear not related to the rest of elements and found that the boundary of non-metals are some semi-metals and its shape is like a “stair”.
