Alexandrov one-point compactification method

A special technique, the Alexandrov one-point compactification method, often used by topologists within a differential-topological framework, has been applied in the proof of the Holographic Electron Density Fragment Theorem [159-161],... 

More details of examples of the chemical applications of the Alexandrov one- point compactification method can be found in Refs. [118] and [159]. 

Based on the tools employed in the Hohenberg-Kohn theorem, also in part on the result of Riess and Miinch, and on a four-dimensional version of the Alexandrov one-point compactification method of topology applied to the complete three-dimensional electron density, it was possible to prove recently that for nondegenerate ground-state electron densities, the Holographic Electron Density Theorem applies any nonzero volume part of the nondegenerate ground-state electron density cloud contains all information about the molecule [4,5]. 

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