The Katětov-Morita theorem for the dimension of metric frames

Abstract

The results which appear here are devoted to the dimension theory of metric frames. We begin by characterizing the covering dimension dim of metric frames in terms of special sequences of covers and then prove the fundamental Katětov-Morita Theorem asserting that Ind L = dim L for every metric frame L.Next, we establish two characterizations of the dimension function Ind in metric frames, one in terms of special bases and another in terms of decompositions into subspaces of dimension zero. These characterizations yield a sum theorem.

Μελέτη Της Θεωρίας Διαστάσεων Στην Περιοχή Των Τοπολογικών Χώρων Και Των Δικτυωτών

“…'Epeita, arketèc ergasÐec pnw se aut th jewrÐa èqoun dhmosieujeÐ, ìpwc twn J. R. Isbell ([59]), B. Banaschewski kai G. Gilmour ( [3]), M. Qaralmpouc ( [20], [21]) kai D. Brijlall kai D. Baboolal ( [9], [10]), prosjètontac stic diastseic aut¸n th mikr epagwgik distash kanonik¸n frames kai th meglh epagwgik distash fusik¸n frames.…”