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Moreover, we study existence of maximal <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\delta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b4<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-separated sets in metric and pseudometric spaces from the point of view the Axiom of Choice and its weaker forms.<\/jats:p>","DOI":"10.1007\/s00153-023-00868-4","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T14:03:39Z","timestamp":1678716219000},"page":"735-749","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The axiom of choice in metric measure spaces and maximal $$\\delta $$-separated sets"],"prefix":"10.1007","volume":"62","author":[{"given":"Micha\u0142","family":"Dybowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Przemys\u0142aw","family":"G\u00f3rka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"issue":"1\u20133","key":"868_CR1","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/S0166-8641(97)00138-7","volume":"85","author":"HL Bentley","year":"1998","unstructured":"Bentley, H.L., Herrlich, H.: Countable choice and pseudometric spaces. 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