Correction: Generalized primal topological spaces

A correction on

Generalized primal topological spaces,

by Hanan Al-Saadi and Huda Al-Malki. AIMS Mathematics, 2023, 8(10): 24162–24175.

DOI:10.3934/math.20231232.

These errata give the following correct statements for the corresponding statements on the cited page of our published article ^[1].

The description of Examples 3.1–3.3 on pages 24165 and 24166 in ^[1] is incomplete, now it is corrected as below:

Example 0.1. Consider $X = \{a, b, c\},$ $\mathfrak{g} = \{\phi, \{a, b\}, \{a, c\}, X\}$ and the primal set $\mathcal{P} = \{\phi, \{a\}, \{b\}, \{a, b\}\}.$ Hence, $(X, \mathfrak{g}, \mathcal{P})$ is a generalized primal topological space.

Example 0.2. Consider

and

Let $A = \{a, b\}.$ Then, $A^\diamond = \{b, c\}.$ Therefore, $A^\diamond \nsubseteq A$ and $A \nsubseteq A^\diamond$.

Example 0.3. Consider

and

Let $A = \{a, b\}$ and $B = \{c\}.$ Then,

Thus, $A^\diamond \cap B^\diamond = \{c\}$ and $(A \cap B)^\diamond = \phi.$ Therefore,

Conflict of interest

The authors declare no conflicts of interest.