Abstract
The most important properties of small inductive dimension (ind) are well known (see, for example, Engelking in Theory of dimensions, finite and infinite, 1995 and Pears in Dimension theory of general spaces, 1975). In this paper, we characterize this dimension of a finite \(\mathrm{T}_0\)-space using matrix algebra. Therefore, using this characterization, we present an algorithm for computing the dimension ind and we compute an upper bound on the number of iterations of the algorithm. Finally, some remarks and open questions are posed.
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Acknowledgments
The authors are grateful to the referee for a number of helpful suggestions that improved the quality of the paper. The third author acknowledges the financial support from the South African NRF, with Grant Ref: IFR2010042800019.
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Communicated by Jinyun Yuan.
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Georgiou, D.N., Megaritis, A.C. & Moshokoa, S.P. A computing procedure for the small inductive dimension of a finite \(\mathrm{T}_0\)-space. Comp. Appl. Math. 34, 401–415 (2015). https://doi.org/10.1007/s40314-014-0125-z
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DOI: https://doi.org/10.1007/s40314-014-0125-z