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A Cantor cube as a space of higher level orderings

In: Tatra Mountains Mathematical Publications, vol. 32, no. 3
Katarzyna Osiak
Detaily:
Rok, strany: 2005, 71 - 84
O článku:
Let $K$ be an ordered field. The set $X (K)$ of its orderings can be topologized to make a Boolean space. Moreover, it has been shown by Craven that for any Boolean space $X$ there exists a field $K$ such that $X(K)$ is homeomorphic to $X$. Especially, the Cantor cube $Dm$ of infinite weight $m$ is homeomorphic to the space of orderings of some field $K$. Becker's higher level ordering is a generalization of the usual concept of ordering. We prove that there exists a field, which space of orderings of fixed level $n$ is homeomorphic to the Cantor cube $Dm$.
Ako citovať:
ISO 690:
Osiak, K. 2005. A Cantor cube as a space of higher level orderings. In Tatra Mountains Mathematical Publications, vol. 32, no.3, pp. 71-84. 1210-3195.

APA:
Osiak, K. (2005). A Cantor cube as a space of higher level orderings. Tatra Mountains Mathematical Publications, 32(3), 71-84. 1210-3195.