Neighborhood base at the identity of free paratopological groups

• Autorzy: Ali Sayed Elfard
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 54E99: None of the above, but in this section
• 54D10: Lower separation axioms ( T 0 -- T 3 , etc.)
• 22A30: Other topological algebraic systems and their representations
• 54H99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2013
• Tom: 1
• Strony: 31-36

Daty

otrzymano

2013-04-10

zaakceptowano

2013-10-01

online

2013-11-12

Twórcy

autor

Ali Sayed Elfard

• Department of Mathematics, University of Zawia, Zawia, Libya,

Bibliografia

• [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.
• [2] A. S. Elfard, Free paratopological groups, (submitted 2013).
• [3] P. Fletcher, and W. F. Lindgren, Quasi-uniform spaces, Lecture Notes in Pure and Applied Mathematic, MarcelDekker Inc., New York, vol. 77 (1982), pp. viii+216.
• [4] J. Marin, and S. Romaguera, A bitopological view of quasi-topological groups, Indian J. Pure Appl. Math. 27 (1996),393–405.
• [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,
• [7] K. Yamada, Characterizations of a metrizable space X such that every An(X) is a k-space, Topology Appl., Topologyand its Applications, vol. 49, (1993), 1, pp. 75–94.

Identyfikatory

DOI

10.2478/taa-2013-0004