Resumen de Una extensión transfinita de la dimensión por recubrimientos

Regino Criado Herrero , Juan Tarrés Freixenet

• 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].