Subgroups of paratopological groups and feebly compact groups
It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup.
It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.
A. V. Arhangel'skii and E. A. Reznichenko, Paratopological and semitopological groups versus topological groups, Topology Appl. 151 (2005), 107-119.
A.V. Arhangel'skii and M. G. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, Vol.1, Atlantis Press and World Scientific, Paris-Amsterdam, 2008.
R. L. Blair, Spaces in which special sets are $z$-embedded, Canad. J. Math. 28, no. 4 (1976), 673-690.
T. Banakh and O. Ravsky, On subgroups of saturated or totally bounded paratopological groups, Algebra Discrete Math. 2003, no.4 (2003), 1-20.
T. Banakh and O. Ravsky, Oscillator topologies on a paratopological group and related number invariants, Algebraic Structures and their Applications, Kyiv: Inst. Mat. NANU (2002), 140-152.
M.Fernández, On some classes of paratopological groups, Topology Proc. 40 (2012), 63-72.
O. Ravsky, Paratopological groups, II, Matematychni Studii, 17 (2002) 93-101.
O. Ravsky, The topological and algebraical properties of paratopological groups, Ph.D. Thesis, Lviv University, 2003 (in Ukrainian).
O. Ravsky, Pseudocompact paratopological groups, arXiv:1003.5343 [Math. GN], September 2013.
E. A. Reznichenko, Extensions of functions defined on products of pseudocompact spaces and continuity of the inverse in pseudocompact groups, Topolology Appl. 59 (1994), 233-244.
S. Romaguera, M. Sanchis and M. Tkachenko, Free paratopological groups, Topology Proc. 27, no. 2 (2003), 613-640.
M. G. Tkachenko, Paratopological and Semitopological Groups vs Topological Groups, Ch.20 in: Recent Progress in General Topology III (K.P.Hart, J.vanMill, P.Simon, Eds.), Atlantis Press, 2014; pp.825-882.
M. G. Tkachenko, G. Delgadillo Piñón and E. Rodríguez Cervera,
A property of powers of the Sorgenfrey line, Q&A in General Topology 27, no. 1 (2009), 45-49.
M. G. Tkachenko and A. H. Tomita, Cellularity in subgroups of paratopological
L.-H. Xie, S. Lin and M. Tkachenko, Factorization properties of paratopological
groups, Topology Appl. 160 (2013), 1902-1917.
Metrics powered by PLOS ALM
Cited-By (articles included in Crossref)
This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site
1. Dense subgroups of paratopological groups
Topology and its Applications vol: 196 first page: 241 year: 2015
Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt