FINITE AND COUNTABLE ADDITIVITY OF TOPOLOGICAL PROPERTIES IN NICE SPACES

Let Q e {character . ANR-property is closely n-additive in X" if X is compact ("closely" means additivity in case Xi is closed in X"). If Q € {metrizability, character < x, pseudocharacter < x, diagonal number < x, /-weight < t , pseudoweight < x, local compactness} then Q is finitely additive in any topological group.