The gap between 𝑐𝑚𝑝𝑋 and 𝑑𝑒𝑓𝑋 can be arbitrarily large

The gap between $\textrm {cmp} X$ and $\textrm {def} X$ can be arbitrarily large
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Proc. Amer. Math. Soc. 102 (1988), 1077-1080

DOI: https://doi.org/10.1090/S0002-9939-1988-0934893-0

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We give an example of a separable metrizable space $X$ with def $X - {\text {cmp}}\;X = n$ for every $n \in \mathbb {N}$.

References

Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
J. de Groot and T. Nishiura, Inductive compactness as a generalization of semi-compactness, Fund. Math. 58 (1966), 201–218. MR 196704, DOI 10.4064/fm-58-2-201-218

Review of R. Pol’s paper

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85b

Keiô Nagami, Dimension theory, Pure and Applied Mathematics, Vol. 37, Academic Press, New York-London, 1970. With an appendix by Yukihiro Kodama. MR 0271918
Roman Pol, A counterexample to J. de Groot’s conjecture $\textrm {cmp}=\textrm {def}$, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), no. 9-10, 461–464 (1983) (English, with Russian summary). MR 703574
Leonard R. Rubin, R. M. Schori, and John J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), no. 1, 93–102. MR 519716, DOI 10.1016/0016-660x(79)90031-x