# Article

Full entry | PDF   (0.1 MB)
Keywords:
universal algebra; paratopological group; topological group
Summary:
Let $(L,\Cal T)$ be a Tychonoff (regular) paratopological group or algebra over a field or ring $K$ or a topological semigroup. If $\operatorname{nw}(L,\Cal T)\leq \tau$ and $\operatorname{nw}(K)\leq\tau$, then there exists a Tychonoff (regular) topology $\Cal T^*\subseteq \Cal T$ such that $w(L,\Cal T^*)\leq\tau$ and $(L,\Cal T^*)$ is a paratopological group, algebra over $K$ or a topological semigroup respectively.
References:
[1] Arhangel'skiĭA.V.: Cardinal invariants of topological groups: Enbeddings and condensations. Dokl. Akad. Nauk SSSR 247 (1979), 779-782. MR 0553825
[2] ArkhangelskiĭA.V., Ponomarev V.I.: Fundamentals of General Topology. D. Reidel Publishing Company, 1984. MR 0785749 | Zbl 0568.54001
[3] Engelking R.: General Topology. Heldermann Verlag, 1989. MR 1039321 | Zbl 0684.54001
[4] Künzi H.A., Romaguera S., Sipacheva O.V.: The Doitchinov completion of a regular paratopological group. Serdica Math. J. 24 (1998), 73-88. MR 1679193
[5] Shakhmatov D.B.: Condensation of universal topological algebras that preserve continuity of operations and decrease weight. Vestnik Mosk. Univ. 39 (1984), 42-45. MR 0741161
[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. MR 1339205
[7] Stephenson R.M.: Minimal topological groups. Math. Ann. 19 (1971), 193-195. MR 0286934 | Zbl 0206.31601
[8] Tkačenko M.G.: Subgroups, quotient groups and products of $\Bbb R$-factorizable groups. Topology Proc. 16 (1991), 201-231. MR 1206464

Partner of