Condensations of Tychonoff universal topological algebras

Constancio Hernández

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 3, page 529-533
  • ISSN: 0010-2628

Abstract

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Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) ≤ τ and nw ( K ) ≤ τ , then there exists a Tychonoff (regular) topology 𝒯 * ⊆ 𝒯 such that w ( L , 𝒯 * ) ≤ τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

How to cite

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Hernández, Constancio. "Condensations of Tychonoff universal topological algebras." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 529-533. <http://eudml.org/doc/248796>.

@article{Hernández2001,
abstract = {Let $(L,\mathcal \{T\})$ be a Tychonoff (regular) paratopological group or algebra over a field or ring $K$ or a topological semigroup. If $\operatorname\{nw\}(L,\mathcal \{T\})\le \tau $ and $\operatorname\{nw\}(K)\le \tau $, then there exists a Tychonoff (regular) topology $\mathcal \{T\}^*\subseteq \mathcal \{T\}$ such that $w(L,\mathcal \{T\}^*)\le \tau $ and $(L,\mathcal \{T\}^*)$ is a paratopological group, algebra over $K$ or a topological semigroup respectively.},
author = {Hernández, Constancio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {universal algebra; paratopological group; topological group; universal algebra; paratopological group; topological group},
language = {eng},
number = {3},
pages = {529-533},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Condensations of Tychonoff universal topological algebras},
url = {http://eudml.org/doc/248796},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Hernández, Constancio
TI - Condensations of Tychonoff universal topological algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 529
EP - 533
AB - Let $(L,\mathcal {T})$ be a Tychonoff (regular) paratopological group or algebra over a field or ring $K$ or a topological semigroup. If $\operatorname{nw}(L,\mathcal {T})\le \tau $ and $\operatorname{nw}(K)\le \tau $, then there exists a Tychonoff (regular) topology $\mathcal {T}^*\subseteq \mathcal {T}$ such that $w(L,\mathcal {T}^*)\le \tau $ and $(L,\mathcal {T}^*)$ is a paratopological group, algebra over $K$ or a topological semigroup respectively.
LA - eng
KW - universal algebra; paratopological group; topological group; universal algebra; paratopological group; topological group
UR - http://eudml.org/doc/248796
ER -

References

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  5. Shakhmatov D.B., Condensation of universal topological algebras that preserve continuity of operations and decrease weight, Vestnik Mosk. Univ. 39 (1984), 42-45. (1984) MR0741161
  6. Shakhmatov D.B., Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension ind, J. Math. Sci. 75 (1995), 3 1754-1769. (1995) MR1339205
  7. Stephenson R.M., Minimal topological groups, Math. Ann. 19 (1971), 193-195. (1971) Zbl0206.31601MR0286934
  8. Tkačenko M.G., Subgroups, quotient groups and products of ℝ -factorizable groups, Topology Proc. 16 (1991), 201-231. (1991) MR1206464

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