There is no compactification theorem for the small inductive dimension |
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| Authors: | Jan van Mill Teodor C Przymusiński |
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| Institution: | Subfaculteir Wiskunde, Vrije Universiteit, De Boelelaan 1081, Amsterdam, The Netherlands;Instytut Matematyczny PAN, Sniadeckich 8, 00-950 Warsaw, Poland |
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| Abstract: | We give an example of a perfectly normal first countable space X1 with ind X1 = 1 such that if Z is a Lindelöf space containing X1. then ind Z=dim Z=∞. Under CH, there is a perfectly normal, hereditarily separable and first countable such space. |
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| Keywords: | 54F45 54D35 |
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