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Topological Field**

A topological field \((k,\mathcal{T},+,\cdot)\) is a topological space \((k,\mathcal{T})\) such that \((k,+,\cdot)\) is a field and \(\cdot,+:k\times k\to k\) are both continuous when \(k\times k\) is endowed with the product topology.