# Almost all submaximal groups are paracompact and σ-discrete

O. Alas; I. Protasov; M. Tkačenko; V. Tkachuk; R. Wilson; I. Yaschenko

Fundamenta Mathematicae (1998)

- Volume: 156, Issue: 3, page 241-260
- ISSN: 0016-2736

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topAlas, O., et al. "Almost all submaximal groups are paracompact and σ-discrete." Fundamenta Mathematicae 156.3 (1998): 241-260. <http://eudml.org/doc/212271>.

@article{Alas1998,

abstract = {We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.},

author = {Alas, O., Protasov, I., Tkačenko, M., Tkachuk, V., Wilson, R., Yaschenko, I.},

journal = {Fundamenta Mathematicae},

keywords = {submaximality; maximality; paracompactness; topological group; separability; σ-discrete; strongly σ-discrete},

language = {eng},

number = {3},

pages = {241-260},

title = {Almost all submaximal groups are paracompact and σ-discrete},

url = {http://eudml.org/doc/212271},

volume = {156},

year = {1998},

}

TY - JOUR

AU - Alas, O.

AU - Protasov, I.

AU - Tkačenko, M.

AU - Tkachuk, V.

AU - Wilson, R.

AU - Yaschenko, I.

TI - Almost all submaximal groups are paracompact and σ-discrete

JO - Fundamenta Mathematicae

PY - 1998

VL - 156

IS - 3

SP - 241

EP - 260

AB - We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.

LA - eng

KW - submaximality; maximality; paracompactness; topological group; separability; σ-discrete; strongly σ-discrete

UR - http://eudml.org/doc/212271

ER -

## References

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