In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.
@article{bwmeta1.element.doi-10_2478_taa-2013-0004, author = {Ali Sayed Elfard}, title = {Neighborhood base at the identity of free paratopological groups}, journal = {Topological Algebra and its Applications}, volume = {1}, year = {2013}, pages = {31-36}, zbl = {1279.22007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0004} }
Ali Sayed Elfard. Neighborhood base at the identity of free paratopological groups. Topological Algebra and its Applications, Tome 1 (2013) pp. 31-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0004/
[1] A. S. Elfard, and P. Nickolas, On the topology of free paratopological groups. II, Topology Appl., vol. 160, no. 1 (2013), pp. 220-229. | Zbl 1291.22007
[2] A. S. Elfard, Free paratopological groups, (submitted 2013). | Zbl 1279.22007
[3] P. Fletcher, and W. F. Lindgren, Quasi-uniform spaces, Lecture Notes in Pure and Applied Mathematic, Marcel Dekker Inc., New York, vol. 77 (1982), pp. viii+216. | Zbl 0501.54018
[4] J. Marin, and S. Romaguera, A bitopological view of quasi-topological groups, Indian J. Pure Appl. Math. 27 (1996), 393–405. | Zbl 0943.54019
[5] V. G. Pestov, Neighborhoods of identity in free topological groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1985), no.3, 8–10, 101.
[6] M. G. Tkacenko, On topologies of free groups, Czechoslovak Mathematical Journal, vol. 34, no. 4, (1984), pp. 541–551, | Zbl 0584.22001
[7] K. Yamada, Characterizations of a metrizable space X such that every An(X) is a k-space, Topology Appl., Topology and its Applications, vol. 49, (1993), 1, pp. 75–94. | Zbl 0817.54020