PreprintarXiv licencearXiv
Proper classes of non-embeddable continua
Abstract
Our main result is a construction of a class H of pathwise connected, locally connected, compact Hausdorff spaces such that (i) if X,Y are distinct spaces in H then a continuous, injective mapping from X to Y does not exist; (ii) H contains 2^k spaces of weight k and size k for every cardinal number k not smaller than the cardinality of the continuum; (iii) if k,l are infinite cardinals and l is not greater than k then H contains 2^k spaces of weight k and size k^l; (iv) the metrizable continua in H are subspaces of the plane.
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BibTeX
@misc{kuba2026proper,
title = {{Proper classes of non-embeddable continua}},
author = {Gerald Kuba},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17173},
eprint = {2609.17173},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17173},
}
RIS
TY - UNPB
TI - Proper classes of non-embeddable continua
AU - Gerald Kuba
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17173
UR - https://arxiv.org/abs/2609.17173
AB - Our main result is a construction of a class H of pathwise connected, locally connected, compact Hausdorff spaces such that (i) if X,Y are distinct spaces in H then a continuous, injective mapping from X to Y does not exist; (ii) H contains 2^k spaces of weight k and size k for every cardinal number k not smaller than the cardinality of the continuum; (iii) if k,l are infinite cardinals and l is not greater than k then H contains 2^k spaces of weight k and size k^l; (iv) the metrizable continua in H are subspaces of the plane.
ER -