Una extensión transfinita de la dimensión por recubrimientos

  1. Criado Herrero, Regino
  2. Tarrés Freixenet, Juan
Revista:
Collectanea mathematica

ISSN: 0010-0757

Año de publicación: 1987

Volumen: 38

Fascículo: 1

Páginas: 77-90

Tipo: Artículo

Otras publicaciones en: Collectanea mathematica

Resumen

We define the $d$-dimension as a transfinite extension of the covering dimension using the Henderson’s method for define the $D$-dimension in [6]. We state the subspace theorem, the locally finite sum theorem and the cartesian product theorem for the $d(X)$-dimension. Also, we state that for every $T_4$ space $X$ we have $d(X)\leq D(X)$ and that these dimensions coincide in the class of metrizable spaces. Also, for every compact metric space $X$ we have $dim(X)\leq D(X)$, where “dim” is the transfinite covering dimension defined in [1].