{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:26:25Z","timestamp":1649039185989},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T00:00:00Z","timestamp":1236124800000},"content-version":"unspecified","delay-in-days":4598,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[1996,8]]},"abstract":"<jats:p>This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff <jats:italic>k-<\/jats:italic>spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure.<\/jats:p>","DOI":"10.1017\/s0960129500001079","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:00:02Z","timestamp":1236157202000},"page":"375-386","source":"Crossref","is-referenced-by-count":0,"title":["Reflexive objects in topological categories"],"prefix":"10.1017","volume":"6","author":[{"given":"Michael D.","family":"Rice","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500001079_ref017","volume-title":"General Topology","author":"Willard","year":"1968"},{"key":"S0960129500001079_ref016","first-page":"215","volume-title":"To H.B. 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