On the structure of topological spaces
| Autor: | Nelson Martins-Ferreira |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Logic Physics::Medical Physics General Topology (math.GN) Group Theory (math.GR) 06F30 54H11 22A15 22A05 17D10 Quantitative Biology::Quantitative Methods preorder fibrous preorder spatial fibrous preorder Cartesian spatial fibrous preorder topological space topological group metric space first-countable space lax-left-associative Mal’tsev operation Computer Science::Logic in Computer Science Mathematics::Category Theory FOS: Mathematics Geometry and Topology Mathematics - Group Theory Mathematical Physics Analysis Computer Science::Formal Languages and Automata Theory Mathematics - General Topology |
| Zdroj: | Axioms; Volume 11; Issue 2; Pages: 49 |
| DOI: | 10.48550/arxiv.2102.09908 |
| Popis: | The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spatial. A special class of spatial fibrous preorders consisting of an interconnected family of preorders indexed by a unitary magma is called Cartesian and is studied here. Topological spaces that are obtained from those fibrous preorders, with a unitary magma I, are called I-Cartesian and are characterized. The characterization reveals a hidden structure on such spaces. Several other characterizations are obtained, and special attention is drawn to the case of a monoid equipped with a topology. A wide range of examples is provided, as well as general procedures to obtain topologies from other data types such as groups and their actions. Metric spaces and normed spaces are considered as well. |
| Databáze: | OpenAIRE |
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