Understanding definitions of Cylinder Topology and Borel Cylinder $\sigma$-algebra.

Question

I'm trying to understand the definition of Cylinder Topology, and Borel Cylinder $\sigma$-algebra, in the picture below, and what it's described in this wikipedia page.

Let $(\mathbb{R}^d)^{\mathbb{T}}=\{\text{functions } f:\mathbb{T}\rightarrow \mathbb{R}^d\}$

By Cylinder Topology I'm understanding the topology obtained from the following basis: $$\text{Basis}=\{A: A=\cap^n_{i=1}\{x_{t_i}\in B_i\} \text{ and } B_i \text{ is an open set of } \mathbb{R}^d \}$$

$\text{Cylinder Topology}=\{\cup_{i \in I} A_i: A_i \in \text{Basis}\}$

where $\cap^n_{i=1}\{x_{t_i}\in B_i\} = \{x \in (\mathbb{R}^d)^{\mathbb{T}}: x_{t_1}\in B_1, \cdots, x_{t_n}\in B_n\}$

and $$ \mathcal{B}((\mathbb{R}^d)^{\mathbb{T}})=\sigma(\text{Cylinder Topology}).$$

Am I understanding these definitions correctly?