Diagonal structures on topological spaces
The author develops some ideas and techniques from his paper [Appl. Gen. Topol. 1, 13-28 (2000; Zbl 0991.54027)]. He investigates when a topological space admits a partial product operation satisfying some rather weak continuity restrictions and almost nothing else, the only algebraic requirement being that some element \(e\) of \(X\) is a left and right identity with respect to this multiplication. The operation is called partial diagonalization of \(X\) at \(e\). Several sufficient conditions for a space to be partially diagonalizable are established. On the other hand, it is shown that certain deep results about the topological structure of compact topological groups can be extended to partially diagonalizable compact spaces. It is also shown that partial diagonalizability playes an important role in some classical topics of general topology. In the final section some open questions are discussed.
scientific article; zbMATH DE number 1879135
scientific article