The discussion centers on the convergence in topological spaces, specifically addressing the condition for a sequence \( x_n \) to converge to a point \( x \) in the context of a metric \( d \). It is established that \( x_n \to_{n\to \infty} x \) if and only if \( d(x_n, x) \to_{n\to \infty} 0 \), assuming \( d \) is a metric. The conversation highlights the importance of defining the metric space clearly, as convergence can vary in non-metrizable topological spaces.
PREREQUISITESMathematicians, students of topology, and anyone interested in the foundational concepts of convergence in both metric and topological spaces.