The Harrison topology is a topology on the set of orderings XF of a formally real field F. Each order can be regarded as a multiplicative group homomorphism from F* onto ±1. Giving ±1 the discrete topology and ±1F the product topology induces the subspace topology on XF. The product is a Boolean space (compact, Hausdorff and totally disconnected), and XF is a closed subset, hence again Boolean.
Read more about this topic: Ordered Field
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—Benjamin Harrison (1833–1901)