Borel $\sigma$-field $\mathcal{B}(C)$

From Wikipidia, a Borel set is any set in a topological space that can be formed from $\mathbf open$ $\mathbf sets$ (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.

Can we take a Borel $\sigma$-field $\mathcal{B}(C)$ , where C represents a Banach space of real-valued continuous functions $\omega$ on [0,1] with $\omega(0)=0.$

Introduction to Stochastic Integration by Hui-Hsiung Kuo, page 24.

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  • In a Banach space, the norm defines a topology, so we then can get a $\sigma$-field from the open sets in the topology. – herb steinberg Dec 7 at 4:14
  • I got confused about the elements of C, and your explanation makes it dawned on me. Thanks! – Peter Van Dec 7 at 12:48