Accumulation Points of Sequence of Distinct Terms in Infinite Particular Point Space/Mistake

Source Work

 * Part $\text {II}$: Counterexamples
 * Section $9 \text { - } 10$: Infinite Particular Point Topology
 * Item $1$
 * Item $1$

Mistake

 * The sequences $\set {a_i}$ which converge are those for which the $a_i \ne p$ are equal for all but a finite number of indices. The only accumulation points for sequences are the points $b_j$ that the $a_i$ equal for infinitely many indices.

Correction
It is essential to clarify that in the sentence:
 * The only accumulation points for sequences are the points $b_j$ that the $a_i$ equal for infinitely many indices.

the sequences in question are specifically those where all $a_i \ne p$.

It is insufficient for complete understanding that the $a_i \ne p$ in the previous question (for which it is not even clear whether it should apply to all terms of $\set {a_i}$ or not) be an implicit condition on the sequences being referred to in the second sentence.

Also see

 * Accumulation Points of Sequence of Distinct Terms in Infinite Particular Point Space