Neighborhood base at the identity of free paratopological groups
Ali Sayed Elfard
Topological Algebra and its Applications, Tome 1 (2013), p. 31-36 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:267462
@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