Geodesic
Some Analogues of Topological Groups
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 171-181.

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Let (G, ∗) be a group and τ be a topology on G. Let τα = A ⊆G : A ⊆ Int(Cl(Int(A))), g ∗ τ = g ∗ A : A ∈ τ for g ∈ G. In this paper, we establish two relations between G and τ under which it follows that g ∗ τ ⊆ τα and g ∗ τα ⊆ τα, designate them by α-topological groups and α-irresolute topological groups, respectively. We indicate that under what conditions an α-topological group is topological group. This paper also covers some general properties and characterizations of α-topological groups and α-irresolute topological groups. In particular, we prove that (1) the product of two α-topological groups is α-topological group, (2) if H is a subgroup of an α-irresolute topological group, then αInt(H) is also subgroup, and (3) if A is an α-open subset of an α-irresolute topological group, then lt; A gt; is also α−open. In the mid of discourse, we also mention about their relationships with some existing spaces.
Keywords: α-open sets, α-closed sets, α-topological groups, α-irresolute topological group 
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Ram, Madhu. Some Analogues of Topological Groups. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 1, pp. 171-181. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_1_a13/

[1] M.S. Bosan, M.D. Khan and L.D.R. Kocinac, On s-Topological groups, Math. Morav. 18 (2014) 35–44. doi:10.5937/MatMor1402035B

[2] M.D. Khan and M.S. Bosan, A note on s-topological groups, Life Sci J. 11 (7s) (2014) 370–374.

[3] M.D. Khan, A. Siab and L.D.R. Kocinac, Irresolute topological groups, Math. Morav. 19 (2015) 73–80. doi:10.5937/MatMor1501073K

[4] M.D. Khan, S. Habib and M.S. Bosan, Quasi S-topological groups, Life Sci. J. 27 (2015) 53–57.

[5] A.S. Mashhour, I.A. Hasanein and S.N. El-Deeb, ɑ-continuous and ɑ-open mappings, Acta Math. Hung. 41 (1983) 213–218. doi:10.1007/BF01961309

[6] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965) 961–970. doi:10.2140/pjm.1965.15.961

[7] R. Noreen and M.D. Khan, Semi-connectedness in s-topological groups, J. Adv. Stud. Topol. 7 (2016). doi:10.20454/jast.2016.1024

[8] R. Noreen, M.S. Bosan and M.D. Khan, Semi-connectedness in irresolute topological groups, Life Sci J. 27 (2015) 4981–1985.

[9] T. Oner, M.B. Kandemir and B. Tanay, Semi-topological groups with respect to semi-continuity and irresoluteness, J. Adv. Stud. Topol. 4 (2013) 23–28. doi:10.20454/jast.2013.626

[10] T. Oner and A. Ozek, On semi topological groups with respect to irresoluteness, Int. J. Recent Sci. Res. 6 (2015) 7914–7916.

[11] T. Oner and A. Ozek, A note on quasi-irresolute topological groups, J. Linear Topol. Algeb. 5 (2016) 41–46.

[12] M. Ram, On almost topological groups, Math. Morav. 23 (2019) 97–106. doi:10.5937/MatMor1901097R

[13] M. Tkachenko, Paratopological and semitopological groups vs topological groups, in: K.P. Hart, J. van Mill, P. Simon (eds.), Recent Progress in General Topology III (Atlantis Press, 2014) 825–882. doi:10.2991/978-94-6239-024-9_20