The dimension of inverse limit and 𝑁-compact spaces

Charalambous, M. G.

doi:10.1090/S0002-9939-1982-0660622-9

The dimension of inverse limit and $N$-compact spaces
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by M. G. Charalambous

Proc. Amer. Math. Soc. 85 (1982), 648-652

DOI: https://doi.org/10.1090/S0002-9939-1982-0660622-9

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Abstract:

For each $k = 1,2, \ldots ,\infty$, $N$, we construct a normal $N$-compact space $X$ with $\dim X = k$, where dim denotes covering dimension, which is the limit space of a sequence of zero-dimensional Lindelöf spaces.

References

M. G. Charalambous, An example concerning inverse limit sequences of normal spaces, Proc. Amer. Math. Soc. 78 (1980), no. 4, 605–607. MR 556641, DOI 10.1090/S0002-9939-1980-0556641-1
Eric K. van Douwen, A technique for constructing honest locally compact submetrizable examples, Topology Appl. 47 (1992), no. 3, 179–201. MR 1192308, DOI 10.1016/0166-8641(92)90029-Y
Ryszard Engelking, Topologia ogólna, Biblioteka Matematyczna [Mathematics Library], vol. 47, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1975 (Polish). MR 0500779

Dimension theory

S. Mrówka, Recent results on $E$-compact spaces, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974, pp. 298–301. MR 0362231
Elżbieta Pol and Roman Pol, A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an $N$-compact space of positive dimension, Fund. Math. 97 (1977), no. 1, 43–50. MR 464179, DOI 10.4064/fm-97-1-51-52
Teodor C. Przymusiński, On the dimension of product spaces and an example of M. Wage, Proc. Amer. Math. Soc. 76 (1979), no. 2, 315–321. MR 537097, DOI 10.1090/S0002-9939-1979-0537097-3
Michael L. Wage, The dimension of product spaces, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4671–4672. MR 507930, DOI 10.1073/pnas.75.10.4671