On δ-Scattered Spaces
The object of the present paper is to introduce the concept of δ-scattered spaces as a natural generalization of the concept of scattered spaces. We prove that the concept of δ-scatteredness of the space coincides with scatteredness. It is noted that scattered need not be δ-scattered in general, also I-space are comparable with δ-scattered space. We start out by giving a characterization of δ-scattered spaces. We study relationships between δ-scatteredness and with scattered, semi-scattered, α-scattered, sub maximal, irresolvable and N-scattered.
A. V. Arhangel’skii and P. J. Collins, On submaximal spaces, Topology and its Applications 64 (1995), 219-241. https://doi.org/10.1016/0166-8641(94)00093-I
C. Chattopadhyay and U. Kumar Roy, δ-sets, irresolvable and resolvable spaces, Math. Slovaca 42(3) (1992), 371-378.
C. Woo, Scattered Space, 2013. https://planetmath.org/scatteredspace
D. Rose, K. Sizemore and B. Thurston, Strongly irresolvable spaces, International J. Math. Math. Sci. 2006 (2006), Article ID 053653, 12 pp. https://doi.org/10.1155/IJMMS/2006/53653
H. Z. Hdeib and C. M. Pareek, A generalization of scattered spaces, Topology Proc. 14 (1989), 59-74.
J. Dontchev and D. Rose, On space whose nowhere dense subset are scattered, International J. Math. Math. Sci. 21 (1998), Article ID 103724, 6 pp. https://doi.org/10.1155/S0161171298001021
J. Dontchev, M. Ganster and D. Rose, α-scattered spaces. II, Houston J. Math. 23 (1997), 231-246.
J. Dontchev, Topological properties defined in terms of generalized open sets, arXiv:math/9811003 [math.GN].
P. Schapira, General Topology, Course at Paris VI University, 2010/2011 (V.3).
R. M. Latif, Topological properties of delta-open sets, Depart. of Math. Sci. King Fahd Univ. of Petroleum and Minerals TR 409 (2009), 1-18.
S. Modak, Relativization in resolvability and irresolvablity, Int. Math. Forum 6 (2011),1059-1064.
T. M. Nour, A note on some applications of semi-open sets, Internat. J. Math. Math. Sci. 21(1) (1998), 205-207. https://doi.org/10.1155/S0161171298000295
T. Noiri, On δ-continuous functions, J. Korean Math. Sci. 16 (1980), 161-166.
V. Kannan and M. Rajagopalan, On scattered spaces, Proc. Amer. Math. Soc. 43 (1974), 402-408. https://doi.org/10.1090/S0002-9939-1974-0334150-X
Z. Aodeh, On contra(δ, gδ)-continuous functions, Univ. of Al-Qadisiyah, J. of Bablylon Univ. Pure and App. Sci. 18(1) (2010), 6-17.
Z. Aodeh, δ-derived and δ-scattered sets, Univ. of Al-Qadisiyah, J. of Al-Qadisiyah for Sci. 20(1) (2015), 192-213.
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