KIKO'S SQUARED BALL

      

      Maybe you though we are in delirious. However, as Lima (1977), in metric space subject the notion of ball is crucial. In a space three different balls could be identified from a metric. There are:

(i)                 Euclidian metrics ;

(ii)               Sum metrics   ; e,

(iii)             Maximum metrics .

 

ball based on Euclidian metrics

ball based on maximum metrics

 

ball based on sum metrics

References:

Any book on Metric Space

(Brazilian reference) LIMA, E.; Espaços Métricos, Instituto de Matemática Pura e Aplicada – IMPA, Rio de Janeiro: Projeto Euclides-CNPq, 299p. 1977