Spaces with noncoinciding dimensions

Charalambous, M. G.

doi:10.1090/S0002-9939-1985-0787903-5

Spaces with noncoinciding dimensions
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by M. G. Charalambous PDF

Proc. Amer. Math. Soc. 94 (1985), 507-515 Request permission

Abstract:

For any given nonnegative integers $l,m,n$ with $\max \{l,m\} \leqslant n$ and $n = 0$ if $m = 0$, we construct a normal, Hausdorff and separable space $X$ with $\operatorname {ind} X = l,\dim X = m$ and $\operatorname {ind} X = n$. We also construct a space ${X_n}$ with $\dim {X_n} = 1$ and $\operatorname {ind} {X_n} = \operatorname {Ind}{X_n} = n$ which is the limit space of an inverse limit sequence of compact, Hausdorff and separable spaces all of whose dimensions are one.

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