无限维空间中的实零点定理

Real Nullstellensatz in Infinite-Dimensional Spaces

在本文中，我们建立了无限维空间中的实零点定理，同时从仿射空间的拓扑结构和域的序结构两个方面，分别刻划了适合无限维实零点定理的序域．此外，本文有例子表明，对任意的基数α，确实存在适合α维实零点定理的序域．

In this paper, we estalbish the real Nullstellensatz in infinite-dimensional spaces, and characterize those ordered fields for which the indnite-dimensional real Nullstellensatz holds via the Zariski topology of affine spaces and the ordering structure of fields respectively. Moreover,it is illustrated by an example that there edests really some ordered field satisfying α-dimensional real Nullstellensatz for an arbitrary cardinal α.