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Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type\u20102 Complexity Theory on the represented spaces. For each of these properties, we give a nice characterization of the class of spaces that are equipped with a representation having the respective property. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310111","type":"journal-article","created":{"date-parts":[[2004,8,18]],"date-time":"2004-08-18T12:02:10Z","timestamp":1092830530000},"page":"443-459","source":"Crossref","is-referenced-by-count":24,"title":["Spaces allowing Type\u20102 Complexity Theory revisited"],"prefix":"10.1002","volume":"50","author":[{"given":"Matthias","family":"Schr\u00f6der","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2004,8,18]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J.Barros\u2010Neto An Introduction to the Theory of Distributions (Marcel Dekker Inc. New York 1973)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1989-15750-9"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0002-9947-1964-0175081-6","article-title":"On sequential convergence","volume":"112","author":"Dudley R. 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