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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