Open AccessAn operation on topological spaces
Author(s) -
A.V. Arhangel'skiı̆
Publication year - 2000
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2000.3021
Subject(s) - mathematics , topological space , topological vector space , product topology , topological algebra , topology (electrical circuits) , diagonalizable matrix , isolated point , space (punctuation) , locally compact space , product (mathematics) , multiplication (music) , pure mathematics , connected space , discrete mathematics , combinatorics , computer science , eigenvalues and eigenvectors , geometry , physics , symmetric matrix , quantum mechanics , operating system
A (binary) product operation on a topological space X is considered. The only restrictions are that some element e of X is a left and a right identity with respect to this multiplication, and that certain natural continuity requirements are satisfied. The operation is called diagonalization (of X). Two problems are considered: 1. When a topological space X admits such an operation, that is, when X is diagonalizable? 2. What are necessary conditions for diagonalizablity of a space (at a given point)? A progress is made in the article on both questions. In particular, it is shown that certain deep results about the topological structure of compact topological groups can be extended to diagonalizable compact spaces. The notion of a Moscow space is instrumental in our study