Geodesic
On cohesive almost zero-dimensional spaces
Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 429-441

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DOI

We investigate C-sets in almost zero-dimensional spaces, showing that closed $\sigma $C-sets are C-sets. As corollaries, we prove that every rim-$\sigma $-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show that these results are sharp, we construct a rim-discrete connected set with an explosion point. We also show that every cohesive almost zero-dimensional subspace of $($Cantor set$)\!\times \mathbb R$ is nowhere dense.
DOI : 10.4153/S0008439520000545
Mots-clés : Almost zero-dimensional, cohesive, rational, Lelek fan, explosion point, Erdős space 
Dijkstra, Jan J.; Lipham, David S. On cohesive almost zero-dimensional spaces. Canadian mathematical bulletin, Tome 64 (2021) no. 2, pp. 429-441. doi: 10.4153/S0008439520000545
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