Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to the predicate.

For certain dense pairs of geometric topological fields without the independence property, whenever the underlying set of a definable group is contained in the dense-codense predicate, the group law is locally definable in the reduct as a geometric topological field. If the reduct has elimination of imaginaries, we extend this result, up to interdefinability, to all groups internal to the predicate.

稠密的几何拓扑场对具有柔和的开放核，也就是说，该对中的每个可定义的开放子集在还原中都已定义。我们修复了范登·德里斯（van den Dries）在o最小组的密集对上的开创性著作的较小版本中的一个小差距，并显示出密集的一对几何拓扑场中的每个可定义的一元函数都与约简中的可定义函数相符。小的可定义子集，即谓词内部的可定义集合。

对于没有独立性的某些稠密的几何拓扑场对，只要在稠密谓词中包含可定义组的基础集，就可以在归约中将组定律局部地定义为几何拓扑场。如果归约法消除了虚构，则可以将此结果扩展到谓词内部的所有组，直至可相互定义。