Somewhat-connectedness and somewhat-continuity in the product space

Subject Areas : General topology

M. S. Bilao ¹ , M. A. Labendia ²

1 - Department of Mathematics and Statistics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines
2 - Department of Mathematics and Statistics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines

Received: 2020-02-14 Accepted : 2020-06-24 Published : 2020-06-01

Keywords: Somewhat-open, somewhat-closed, somewhat-connected, somewhat-continuous,

Abstract :

In this paper, the concept of somewhat-connected space will be introduced and characterized. Its connection with the other well-known concepts such as the classical connectedness, the $\omega_\theta$-connectedness, and the $\omega$-connectedness will be determined. Moreover, the concept of \textit{somewhat}-continuous function from an arbitrary topological space into the product space will be characterized.

References:

[1] T. A. Al-Hawary, On supper continuity of topological spaces, Matematika. 21 (2005), 43-49.

[2] K. Al-Zoubi, K. Al-Nashef, The topology of ω-open subsets, Al-Manarah Journal. 9 (2003), 169-179.

[3] H. Aljarrah, M. Md Noorani, T. Noiri, Contra ωβ-continuity, Bol. Soc. Parana. Mat. 32 (2014), 9-22.

[4] H. Aljarrah, M. Md Noorani, T. Noiri, On generalized ωβ-closed sets, Missouri J. Math. Sci. 26 (2014), 70-87.

[5] C. W. Baker, An alternate form of somewhat continuity, Inter. J. Contemporary Math. Sci. 10 (2015), 57-64.

[6] C. W. Baker, Somewhat open sets, Gen. Math. Notes. 34 (2016), 29-36.

[7] M. Caldas, S. Jafari, M. M. Kovar, Some properties of θ-open sets, Divulg. Mat. 12 (2004), 161-169.

[8] M. Caldas, S. Jafari, R. M. Latif, Sobriety via θ-open sets, An. Stii¸ nt. Univ. Al. I. Cuza Iasi. Mat. (N.S.). 56 (2010), 163-167.

[9] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, On upper and lower almost contra-ω-continuous multi-functions, Ital. J. Pure Appl. Math. 32 (2014), 445-460.

[10] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Properties of faintly ω-continuous functions, Bol. Mat. 20 (2013), 135-143.

[11] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Some properties of upperlower ω-continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform. 23 (2013), 35-55.

[12] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Somewhat ω-continuous functions, Sarajevo J. Math. 11 (2015), 131-137.

[13] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Upper and lower ω-continuous multifunctions, Afr. Mat. 26 (2015), 399-405.

[14] H. Darwesh, Between preopen and open sets in topological spaces, Thai J. Math. 11 (2013), 143-155.

[15] R. F. Dickman, J. R. Porter, θ-closed subsets of Hausdorff spaces, Pacific J. Math. 59 (1975), 407-415.

[16] R. F. Dickman, J. R. Porter, θ-perfect and θ-absolutely closed functions, Illinois J. Math. 21 (1977), 42-60.

[17] E. Ekici, S. Jafari, R. M. Latif, On a finer topological space than τθand some maps, Ital. J. Pure Appl. Math. 27 (2010), 293-304.

[18] H. Z. Hdeib, ω-closed mappings, Rev. Colombiana Mat. 1-2 (1982), 65-78.

[19] H. B. Hoyle, K. R. Gentry, Somewhat continuous functions, Czech. Math. Journal. 21 (1971), 5-12.

[20] D. S. Jankovic, θ-regular spaces, Internat. J. Math. & Math. Sci. 8 (1986), 615-619.

[21] J. E. Joseph, θ-closure and θ-subclosed graphs, Math. Chronicle. 8 (1979), 99-117.

[22] M. M. Kovar, On θ-regular spaces, Internat. J. Math. & Math. Sci. 17 (1994), 687-692.

[23] M. Labendia, J. A. Sasam, On ω-connectedness and ω-continuity in the product space, European J. of Pure & Appl. Math. 11 (2018), 834-843.

[24] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70 (1963), 36-41.

[25] P. E. Long, L. L. Herrington, The τθ-topology and faintly continuous functions, Kyungpook Math. J. 22 (1982), 7-14.

[26] T. Noiri, S. Jafari, Properties of (θ,s)-continuous functions, Topology Appl. 123 (2002), 167-179.

[27] N. Velicko, H-closed topological spaces, Trans. Am. Math. Soc. 78 (1968), 103-118.