On Γ-embeddings and partial actions of function spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913037852606464 |
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| author | Martínez-Sánchez, Luis A. Pinedo, Héctor Vilca-Rodríguez, José L. |
| author_facet | Martínez-Sánchez, Luis A. Pinedo, Héctor Vilca-Rodríguez, José L. |
| contents | This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open subsets of a topological space. We describe several embeddings of this type, referred to as $Γ$- embeddings, and we place particular emphasis on one of them. In particular, we prove that every topological space $Y$ admits a $Γ$-embedding into the space of continuous functions $C(X, Y )$, equipped with the compact-open topology, where $X$ is a compact space. Consequently, any partial action $θ$ of a topological group $G$ on $ Y$ naturally induces a partial action $\hatθ$ on $C(X, Y ).$ Throughout the paper, we investigate various relationships between these actions, as well as between their corresponding globalizations and enveloping spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Γ-embeddings and partial actions of function spaces Martínez-Sánchez, Luis A. Pinedo, Héctor Vilca-Rodríguez, José L. General Topology This paper deals with the extension of partial actions of topological groups on topological spaces. Within this framework, we introduce a class of topological embeddings defined via the inverse semigroup of homeomorphisms between open subsets of a topological space. We describe several embeddings of this type, referred to as $Γ$- embeddings, and we place particular emphasis on one of them. In particular, we prove that every topological space $Y$ admits a $Γ$-embedding into the space of continuous functions $C(X, Y )$, equipped with the compact-open topology, where $X$ is a compact space. Consequently, any partial action $θ$ of a topological group $G$ on $ Y$ naturally induces a partial action $\hatθ$ on $C(X, Y ).$ Throughout the paper, we investigate various relationships between these actions, as well as between their corresponding globalizations and enveloping spaces. |
| title | On Γ-embeddings and partial actions of function spaces |
| topic | General Topology |
| url | https://arxiv.org/abs/2601.14545 |