A remark on asymptotic dimension and digital dimension of finite metric spaces
Vitalij A. Chatyrko, Mykhailo Zarichnyi · Matematychni Studii · 2007
A remark on asymptotic dimension and digital dimension of finite metric spaces , Matematychni Studii, 27 (2007) 100104.Relationships between the asymptotic dimension (in the sense of Gromov) of a proper metric space and the so-called digital dimension of its finite subspaces are established.Â. ×àòûðêî, Ì. Çàðè÷íûé.Çàìå÷àíèå îá àñèìïòîòè÷åñêîé è öèôðîâîé ðàçìåðíîñòÿõ êîíå÷íûõ ìåòðè÷åñêèõ ïðîñòðàíñòâ // Ìàòåìàòè÷íi Ñòóäi¨.2007.Ò.27, 1. C.100 104.Óòàíàâëèâàþòñÿ ñîîòíîøåíèÿ ìåæäó àñèìïòîòè÷åñêîé ðàçìåðíîñòüþ (â ñìûñëå Ãðîìîâà) ñîáñòâåííîãî ìåòðè÷åñêîãî ïðîñòðàíñòâà è òàê íàçûâàåìîé öèôðîâîé ðàçìåðíîñòüþ åãî êîíå÷íûõ ïîäïðîñòðàíñòâ.