# Neighborhood base at the identity of free paratopological groups

Topological Algebra and its Applications (2013)

- Volume: 1, page 31-36
- ISSN: 2299-3231

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topAli Sayed Elfard. "Neighborhood base at the identity of free paratopological groups." Topological Algebra and its Applications 1 (2013): 31-36. <http://eudml.org/doc/267462>.

@article{AliSayedElfard2013,

abstract = {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.},

author = {Ali Sayed Elfard},

journal = {Topological Algebra and its Applications},

keywords = {group; free paratopological group; neighborhood base at the identity; fine uniformity; fine quasi-uniformity; Alexandroff space; topological group; paratopological group; free topological group},

language = {eng},

pages = {31-36},

title = {Neighborhood base at the identity of free paratopological groups},

url = {http://eudml.org/doc/267462},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Ali Sayed Elfard

TI - Neighborhood base at the identity of free paratopological groups

JO - Topological Algebra and its Applications

PY - 2013

VL - 1

SP - 31

EP - 36

AB - 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.

LA - eng

KW - group; free paratopological group; neighborhood base at the identity; fine uniformity; fine quasi-uniformity; Alexandroff space; topological group; paratopological group; free topological group

UR - http://eudml.org/doc/267462

ER -

## References

top- [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. Zbl1291.22007
- [2] A. S. Elfard, Free paratopological groups, (submitted 2013). Zbl1279.22007
- [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. Zbl0501.54018
- [4] J. Marin, and S. Romaguera, A bitopological view of quasi-topological groups, Indian J. Pure Appl. Math. 27 (1996), 393–405. Zbl0943.54019
- [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, Zbl0584.22001
- [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. Zbl0817.54020

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