{"paper":{"title":"Compactly generated spaces and quasi-spaces in topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CT","authors_text":"Willian Ribeiro","submitted_at":"2019-08-12T17:56:39Z","abstract_excerpt":"The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category $\\mathsf{Top}$ of topological spaces and continuous functions, to study $\\textit{compactly generated spaces}$ and $\\textit{quasi-spaces}$ in this setting. Moreover, for a class $\\mathcal{C}$ of objects we generalize the notion of $\\textit{$\\mathcal{C}$-generated spaces}$, from which we derive, for instance, a general concept of $\\textit{Alexandroff spaces}$. Furthermore, as done for $\\mathsf{Top}$, we also study, in our level of generality, the relationship bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04287","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04287/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}