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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.14235 |
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| _version_ | 1866908486072270848 |
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| author | Pol, Roman Reńska, Mirosława |
| author_facet | Pol, Roman Reńska, Mirosława |
| contents | We shall prove that if X, Y are compact metrizable spaces of positive dimension and h: X x Y --> X is a continuous map with zero-dimensional fibers then X contains a non-trivial continuum without one-dimensional subsets; in particular X is not a countable union of zero-dimensional sets, which provides a negative answer to a question of J. Dudák and B. Vejnar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | No product of two non-trivial countable-dimensional continua maps lightly into any of the factors Pol, Roman Reńska, Mirosława General Topology We shall prove that if X, Y are compact metrizable spaces of positive dimension and h: X x Y --> X is a continuous map with zero-dimensional fibers then X contains a non-trivial continuum without one-dimensional subsets; in particular X is not a countable union of zero-dimensional sets, which provides a negative answer to a question of J. Dudák and B. Vejnar. |
| title | No product of two non-trivial countable-dimensional continua maps lightly into any of the factors |
| topic | General Topology |
| url | https://arxiv.org/abs/2503.14235 |