What is the (genuine) name for the Gutik hedgehog?

Question

Working with non-regular topological semigroups, my collegue Oleg Gutik discovered a special space $H$ which we named Gutik's hedgehog. It is homeomorphic to the space $$H:=\{(0,0)\}\cup\{(\tfrac1n,0):n\in\mathbb N\}\cup\{(\tfrac1n,\tfrac1{nm}):n,m\in\mathbb N\},$$ endowed with the topology $\tau$ consisting of sets $U\subset H$ satisfying the following two conditions:

(1) if $(\frac1n,0)\in U$ for some $n\in\mathbb N$, then there exists $m\in\mathbb N$ such that $(\frac1n,\frac1{nk})\in U$ for all $k\ge m$;

(2) if $(0,0)\in U$, then there exists $m\in\mathbb N$ such that $(\frac1n,\frac1{nk})\in U$ for all $n\ge m$ and all $k\in\mathbb N$.

It turns out that Gutik's hedgehog is a test space for regularity in the class of first-countable Hausdorff spaces.

Theorem. A first-countable Hausdorff space is regular if and only if it contains no topological copies of the Gutik hedgehog.

Because of this fundamental role in testing regularity, I admit that Gutik's hedgehog is known in topology under some different name. I would be grateful for any information in this respect.

Remark 1. The Gutik's hedgehog resembles (but is not equal to) the non-regular space of Smirnov, see Example 64 in "Counterexamples in Topology".

Answer 1

Searching Steen & Seebach, Counterexamples in Topology for "Hausdorff, separable, not regular" I found this example. Is that it?

This is Example 79, page 97.

Irregular Lattice Topology
Let $A = \{(i,k) : 0 < i,k \in \mathbb{N}\}$, $B = \{(i,0) : i \geq 0\}$ and $X = A \cup B$. Declare each point of $A$ to be open. Let the set of all $U_n((i,0)) = \{(i,k) : k=0$ or $k \geq n\}$ form a local basis at any point with $i \neq 0$ and the set of all $V_n = \{(i,k) : i=k=0$ or $i,k\geq n\}$ be a local basis at $(0,0)$.