{"paper":{"title":"On dimensions modulo a compact metric ANR and modulo a simplicial complex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GN","authors_text":"Jerzy Krzempek","submitted_at":"2012-03-20T20:57:43Z","abstract_excerpt":"V. V. Fedorchuk has recently introduced dimension functions K-dim \\leq K-Ind and L-dim \\leq L-Ind, where K is a simplicial complex and L is a compact metric ANR. For each complex K with a non-contractible join |K| * |K| (we write |K| for the geometric realisation of K), he has constructed first countable, separable compact spaces with K-dim < K-Ind.\n  In a recent paper we have combined an old construction by P. Vop\\v{e}nka with a new construction by V. A. Chatyrko, and have assigned a certain compact space Z (X, Y) to any pair of non-empty compact spaces X, Y. In this paper we investigate the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4581","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":""},"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"}