Definition of Gustin's sequence space is incorrect

[Moniker1998]

https://topology.pi-base.org/spaces/S000122

The only difference is the first two paragraphs which are supposed to be as follows:

Let $\mathbb{Z}^+$ denote the set of positive integers, $Y$ be the set of all finite even sequences of positive integers, $W = \{A \subset Y\ |\ |A| = 2\}$. Gustin's Sequence Space is the set $X = Y \cup (\mathbb{Z}^+ \times W)$ with topology defined as follows:

For any $\alpha, \beta \in (\mathbb{Z}^+)^{<\omega}$, let $\alpha \cap \beta$ be the sequence formed by adjoining $\beta$ to the end of $\alpha$. Let $\alpha \geq i \in \mathbb{Z}$ abbreviate $a \geq i$ for every $a \in \alpha$. Let $\beta \supset_i \alpha$ abbreviate $\exists \gamma \geq i$ with $\beta = \alpha\gamma$ and $U_i(\alpha) = \{\beta \in Y\ |\ \beta \supset_i \alpha\}$.

Here, even refers to even length.

[Moniker1998]

Note that its important that $Y$ consists of even sequences - otherwise we wouldn't be able to show that $X$ is Hausdorff.