Absorbing systems in the Hilbert cube related to Hausdorf and covering dimension

Анотація

The topology of the system $(D^{>\gamma_n}_{\ge k}(Q))_{k\in\mathbb N\cup\{0\},\gamma_n\in\Gamma,\gamma_{n+1}\ge k}$, where $D^{>\gamma_n}_{\ge k}(Q)=\{A\in exp(Q)\mid dim_H(A)>\gamma_n,dim(A)\ge k\}$ and $\Gamma=\{\gamma_i\}_{i=1}^\infty$ is a countable ordered set with $0<\gamma_1<\gamma_2<\dots<\infty$, is described.

Описано топологію системи $(D^{>\gamma_n}_{\ge k}(Q))_{k\in\mathbb N\cup\{0\},\gamma_n\in\Gamma,\gamma_{n+1}\ge k}$, де $D^{>\gamma_n}_{\ge k}(Q)=\{A\in exp(Q)\mid dim_H(A)>\gamma_n,dim(A)\ge k\}$ and $\Gamma=\{\gamma_i\}_{i=1}^\infty$ і $\Gamma=\{\gamma_i\}_{i=1}^\infty$ – зліченна впорядкована множина така, що $0<\gamma_1<\gamma_2<\dots<\infty$.