Continuous functions on primal topological spaces induced by group actions
If $ G $ is a group acting on a set $ X $, then for any $ a\in G $, the restriction $ \phi_a:X\to X $ of the action to $ a $ induces a topology $ \tau_a $ for $ X $, called the primal topology induced by $ \phi_a $. First, we obtain a characterization of the normal subgroups in terms of the prima...
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AIMS Press
2025-01-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025037 |
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| author | Luis Fernando Mejías Jorge Vielma Elvis Aponte Lourival Rodrigues De Lima |
| author_facet | Luis Fernando Mejías Jorge Vielma Elvis Aponte Lourival Rodrigues De Lima |
| author_sort | Luis Fernando Mejías |
| collection | DOAJ |
| description | If $ G $ is a group acting on a set $ X $, then for any $ a\in G $, the restriction $ \phi_a:X\to X $ of the action to $ a $ induces a topology $ \tau_a $ for $ X $, called the primal topology induced by $ \phi_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, \tau_{ \phi_x}) $. In particular, we prove the continuity of some maps when $ a, b, q\in G $ satisfy a quantum type relation, $ ba = qab $, as is in the quaternion and Heisenberg groups. |
| format | Article |
| id | doaj-art-ef66a67186a8482da3da1e609b9529de |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ef66a67186a8482da3da1e609b9529de2025-08-20T02:48:13ZengAIMS PressAIMS Mathematics2473-69882025-01-0110179380810.3934/math.2025037Continuous functions on primal topological spaces induced by group actionsLuis Fernando Mejías0Jorge Vielma1Elvis Aponte2Lourival Rodrigues De Lima3Departamento de Matemáticas, Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, ESPOL, Campus Gustavo Galindo, km. 30.5 vía Perimetral, Guayaquil, 090902, EcuadorDepartamento de Matemáticas, Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, ESPOL, Campus Gustavo Galindo, km. 30.5 vía Perimetral, Guayaquil, 090902, EcuadorDepartamento de Matemáticas, Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, ESPOL, Campus Gustavo Galindo, km. 30.5 vía Perimetral, Guayaquil, 090902, EcuadorDepartamento de Matemáticas, Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, ESPOL, Campus Gustavo Galindo, km. 30.5 vía Perimetral, Guayaquil, 090902, EcuadorIf $ G $ is a group acting on a set $ X $, then for any $ a\in G $, the restriction $ \phi_a:X\to X $ of the action to $ a $ induces a topology $ \tau_a $ for $ X $, called the primal topology induced by $ \phi_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, \tau_{ \phi_x}) $. In particular, we prove the continuity of some maps when $ a, b, q\in G $ satisfy a quantum type relation, $ ba = qab $, as is in the quaternion and Heisenberg groups.https://www.aimspress.com/article/doi/10.3934/math.2025037group actionprimal topologycontinuous function |
| spellingShingle | Luis Fernando Mejías Jorge Vielma Elvis Aponte Lourival Rodrigues De Lima Continuous functions on primal topological spaces induced by group actions AIMS Mathematics group action primal topology continuous function |
| title | Continuous functions on primal topological spaces induced by group actions |
| title_full | Continuous functions on primal topological spaces induced by group actions |
| title_fullStr | Continuous functions on primal topological spaces induced by group actions |
| title_full_unstemmed | Continuous functions on primal topological spaces induced by group actions |
| title_short | Continuous functions on primal topological spaces induced by group actions |
| title_sort | continuous functions on primal topological spaces induced by group actions |
| topic | group action primal topology continuous function |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025037 |
| work_keys_str_mv | AT luisfernandomejias continuousfunctionsonprimaltopologicalspacesinducedbygroupactions AT jorgevielma continuousfunctionsonprimaltopologicalspacesinducedbygroupactions AT elvisaponte continuousfunctionsonprimaltopologicalspacesinducedbygroupactions AT lourivalrodriguesdelima continuousfunctionsonprimaltopologicalspacesinducedbygroupactions |