Can You Help Me Interpret the Meaing of an Relationship between a Vector, Element Symbol, the All Real Values Symbol, and a Variable?

Question

I'm reading a research paper and I'm trying to decipher some mathematical text.

It looks like this: $[y_1,...,y_T] \in \mathbb{R}^T$

My best guess is it is saying, "This set contains all real values T."

I know:

1. On the left-hand side, I am looking at a vector where y is a variable contained in the vector.
2. $y_1$ is the first element.
3. $y_T$ is the last element
4. The vector $[y_1,...,y_T]$ contains all the elements of y up to a given value T. In this paper T is defined as a specific point in the time series. This implies that the vector contains all the values from the beginning of time 1 to a pre-determined time T.
5. $\in$ is the element symbol.
6. $\mathbb{R}$ is mean all real values.

Help me understand:

1. What $\mathbb{R}^T$ means.
2. How $\mathbb{R}^T$ relates to that vector.
3. Where I lack in my understanding of how I defined this relationship.