Geodesic
A Note on Inverse Limits of Finite Spaces
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 69-70

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The following lemma, which appears as Lemma 4 in [5], was used to determine certain multicoherence properties of inverse limits of continua. Lemma. Let X denote the inverse limit of an inverse system {X λ, f λμ, Λ} of compact Hausdorff spaces X λ. If X λ has no more than k components (where k < ∞ is fixed) for each λ ∊ Λ, then X has no more than k components.In this paper we give a set theoretic analogue of this lemma and an extension which was suggested to the author by Professor F. W. Lawvere. An application to inverse limits of finite groups is then given. 
Jr, S. B. Nadler. A Note on Inverse Limits of Finite Spaces. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 69-70. doi: 10.4153/CMB-1970-014-7
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     title = {A {Note} on {Inverse} {Limits} of {Finite} {Spaces}},
     journal = {Canadian mathematical bulletin},
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     year = {1970},
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     number = {1},
     doi = {10.4153/CMB-1970-014-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-014-7/}
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