@article{Mejías2025, 
author = {Luis Fernando Mejías and Jorge Vielma and Elvis Aponte and Lourival Rodrigues De Lima},
title = {Continuous functions on primal topological spaces induced by group actions},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {793-808},
keywords = {continuous function, group action, primal topology},
url = {https://www.sciopen.com/article/10.3934/math.2025037},
doi = {10.3934/math.2025037},
abstract = {If    G is a group acting on a set    X, then for any    a  ∈  G, the restriction        ϕ    a    :  X  →  X of the action to    a induces a topology        τ    a   for    X, called the primal topology induced by        ϕ    a  . First, we obtain a characterization of the normal subgroups in terms of the primal topologies. Later, we prove that some commutative relations among elements on the group    G determine the continuity of maps among different primal spaces    (  X  ,      τ                  ϕ        x              ). In particular, we prove the continuity of some maps when    a  ,  b  ,  q  ∈  G satisfy a quantum type relation,    b  a  =  q  a  b, as is in the quaternion and Heisenberg groups.}
}