{"paper":{"title":"A choice-free approach to Wallman compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Cerene Rathilal, Ranjitha Raviprakash, Sebastian D Melzer","submitted_at":"2026-06-04T08:10:36Z","abstract_excerpt":"The classical Wallman compactification of a $T_1$-space and the Stone--\\v{C}ech compactification of a completely regular space rely on choice principles. We show that, by representing a space by its powerset MT-algebra (McKinsey--Tarski algebra), both constructions admit choice-free compactifications. More generally, from any Wallman basis of a spatial $T_1$ MT-algebra we construct a compact $T_1$ MT-algebra which is a compactification of the original algebra. Taking the basis of all closed elements yields a choice-free Wallman compactification of every spatial $T_1$ MT-algebra, while taking t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05832","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/2606.05832/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"}