Abstract
In this paper, we introduce and study strongly \(n\)-homogeneous, \(n\)-homogeneous and locally homogeneous generalized topological spaces. We give many properties, examples and counterexamples concerning these concepts. In particular, we give several results of finite \(n\)-homogeneous generalized topological spaces.
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References
Al Ghour S (2003) Minimality and prehomogeneity. Acta Math Univ Comen (N.S.) 72(2):237–244
Al Ghour S (2004) Components and local prehomogeneity. Acta Mathematica Universitatis Comenianae (N.S.) 73(2):187–196
Al Ghour S, Al Khatib N (2011) On slight homogeneous and countable dense homogeneous spaces. Mat Vesn 63(2):133–144
Al Ghour S, Zoubi K, Fora A (2005) Semihomogeneous topological spaces. Publ Math Debr 67(2):131–142
Al Ghour S, Al-Omari A, Noiri T (2013) On homogeneity and homogeneity components in generalized topological spaces. Filomat 27(6):1097–1105
Al-Omari A, Noiri T (2012) A unified theory of contra-(μ, λ)-continuous functions in generalized topological spaces. Acta Math Hung 135(1–2):31–41
Anderson RD (1958) A characterization of the universal curve and a proof of its homogeneity. Ann Math 67(2):313–324
Bales JW (1976) Representable and strongly locally homogeneous spaces and strongly n-homogeneous spaces. Houst J Math 2:315–327
Bennett R (1972) Countable dense homogeneous spaces. Fundam Math 74(3):189–194
Brouwer LEJ (1913) Some remarks on the coherence type. Proc Akad Amst 15:1256–1263
Cao C, Yan J, Wang W, Wang B (2013) Some generalized continuities functions on generalized topological spaces. Hacet J Math Stat 42(2):159–163
Cho SK (1996) Some results related to densely homogeneous spaces. Commun Korean Math Soc 11(4):1061–1066
Császár Á (2002) Generalized topology, generalized continuity. Acta Math Hung 96:351–357
Császár Á (2003) γ-connected sets. Acta Math Hung 101:273–279
Császár Á (2004) Extermally disconnected generalized topologies. Annales Universitatis Scientiarium Budapestinensis de Rolando Eotvos Nominatae. Sectio Mathematica 47:91–96
Császár Á (2009) Products of generalized topologies. Acta Math Hung 123:127–132
Dantzig D (1930) Uber topologisch homogene continua. Fundam Math 15:102–125
Fitzpatrick B Jr, Zhou HX (1992) Countable dense homogeneity and the Baire property. Topol Appl 43(1):1–14
Fora A (2000) New and old types of homogeneity. Turk J Math 24(4):335–344
Ford LR (1954) Homeomorphism groups and coset spaces. Trans Am Math Soc 77:490–497
Fort MK (1962) Homogeneity of infinite products of manifolds with boundary. Pac J Math 12:879–884
Jayanthi D (2012) Contra continuity on generalized topological spaces. Acta Math Hung 137(4):263–271
Kim YK, Min WK (2012a) On operations induced by hereditary classes on generalized topological spaces. Acta Math Hung 137(1–2):130–138
Kim YK, Min WK (2012b) R(g, g′)—continuity on generalized topological spaces. Commun Korean Math Soc 27(4):809–813
Korczak-Kubiak E, Loranty A, Pawlak RJ (2013) Baire generalized topological spaces, generalized metric spaces and infinite games. Acta Math Hung 140(3):203–231
Mill JV (1982) Strong local homogeneity does not imply countable dense homogeneity. Proc Am Math Soc 84(1):143–148
Patkowska H (1989) On 1/2-homogeneous ANR-spaces. Fundamenta Mathematicae 132(1):25–58
Renukadevi V, Vimaladevi P (2014) Note on generalized topological spaces with hereditary classes. Boletim da Sociedade Paranaense de Matematica 32(1):89–97
Sierpenski W (1920) Sur uniproprit’te’ topologique des ensembles de’nombrable dense en soi. Fundamenta Mathematicae 1:11–28
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Al Ghour, S.H., Al-Deiakeh, R.M. n-Homogeneous and LH Generalized Topological Spaces. Iran J Sci Technol Trans Sci 42, 73–79 (2018). https://doi.org/10.1007/s40995-018-0487-y
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DOI: https://doi.org/10.1007/s40995-018-0487-y