Geodesic
Localic Katětov-Tong insertion theorem and localic Tietze extension theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 801-814

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In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.
Classification : 06D20, 06D22, 18B30, 54C20, 54C30
Keywords: frame; locale; lower (upper) continuous chain; normal locale 
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     author = {Li, Yong Min and Guo-jun, Wang},
     title = {Localic {Kat\v{e}tov-Tong} insertion theorem and localic {Tietze} extension theorem},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {801--814},
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     year = {1997},
     mrnumber = {1603726},
     zbl = {0938.06008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a14/}
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Li, Yong Min; Guo-jun, Wang. Localic Katětov-Tong insertion theorem and localic Tietze extension theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 801-814. http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a14/