Bilao, M. S.; Labendia, M. A. Somewhat-connectedness and somewhat-continuity in the product space. (English) Zbl 1442.54017 J. Linear Topol. Algebra 9, No. 2, 139-148 (2020). Summary: 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 somewhat-continuous function from an arbitrary topological space into the product space will be characterized. MSC: 54D05 Connected and locally connected spaces (general aspects) 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54A05 Topological spaces and generalizations (closure spaces, etc.) Keywords:somewhat-open; somewhat-closed; somewhat-connected; somewhat-continuous PDFBibTeX XMLCite \textit{M. S. Bilao} and \textit{M. A. Labendia}, J. Linear Topol. Algebra 9, No. 2, 139--148 (2020; Zbl 1442.54017) 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 ofω-open subsets, Al-Manarah Journal. 9 (2003), 169-179. [3] H. Aljarrah, M. Md Noorani, T. Noiri, Contraωβ-continuity, Bol. Soc. Parana. Mat. 32 (2014), 9-22. · Zbl 1412.54030 [4] H. Aljarrah, M. Md Noorani, T. Noiri, On generalizedωβ-closed sets, Missouri J. Math. Sci. 26 (2014), 70-87. · Zbl 1300.54020 [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 ofθ-open sets, Divulg. Mat. 12 (2004), 161-169. · Zbl 1099.54501 [8] M. Caldas, S. Jafari, R. M. Latif, Sobriety viaθ-open sets, An. Stii¸nt. Univ. Al. I. Cuza I¸asi. Mat. (N.S.). 56 (2010), 163-167. · Zbl 1199.54057 [9] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, On upper and lower almost contra-ω-continuous multifunctions, Ital. J. Pure Appl. Math. 32 (2014), 445-460. · Zbl 1330.54030 [10] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Properties of faintlyω-continuous functions, Bol. Mat. 20 (2013), 135-143. · Zbl 1338.54079 [11] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Some properties of upperlowerω-continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform. 23 (2013), 35-55. · Zbl 1313.54044 [12] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Somewhatω-continuous functions, Sarajevo J. Math. 11 (2015), 131-137. · Zbl 1326.54022 [13] C. Carpintero, N. Rajesh, E. Rosas, S. Saranyasri, Upper and lowerω-continuous multifunctions, Afr. Mat. 26 (2015), 399-405. · Zbl 1320.54013 [14] H. Darwesh, Between preopen and open sets in topological spaces, Thai J. Math. 11 (2013), 143-155. · Zbl 1276.54003 [15] R. F. Dickman, J. R. Porter,θ-closed subsets of Hausdorff spaces, Pacific J. Math. 59 (1975), 407-415. · Zbl 0314.54023 [16] R. F. Dickman, J. R. Porter,θ-perfect andθ-absolutely closed functions, Illinois J. Math. 21 (1977), 42-60. · Zbl 0351.54010 [17] E. Ekici, S. Jafari, R. M. Latif, On a finer topological space thanτθand some maps, Ital. J. Pure Appl. Math. 27 (2010), 293-304. · Zbl 1238.54001 [18] H. Z. Hdeib,ω-closed mappings, Rev. Colombiana Mat. 1-2 (1982), 65-78. · Zbl 0574.54008 [19] H. B. Hoyle, K. R. Gentry, Somewhat continuous functions, Czech. Math. Journal. 21 (1971), 5-12. · Zbl 0222.54010 [20] D. S. Jankovic,θ-regular spaces, Internat. J. Math. & Math. Sci. 8 (1986), 615-619. · Zbl 0577.54012 [21] J. E. Joseph,θ-closure andθ-subclosed graphs, Math. Chronicle. 8 (1979), 99-117. 148M. S. Bilao and M. A. Labendia / J. Linear. Topological. Algebra.09(02) (2020)139-148. [22] M. M. Kovar, Onθ-regular spaces, Internat. J. Math. & Math. Sci. 17 (1994), 687-692. · Zbl 0809.54017 [23] M. Labendia, J. A. Sasam, Onω-connectedness andω-continuity in the product space, European J. of Pure & Appl. Math. 11 (2018), 834-843. · Zbl 1413.54056 [24] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Month. 70 (1963), 36-41. · Zbl 0113.16304 [25] P. E. Long, L. L. Herrington, Theτθ-topology and faintly continuous functions, Kyungpook Math. J. 22 (1982), 7-14. · Zbl 0486.54009 [26] T. Noiri, S. Jafari, Properties of (θ, s)-continuous functions, Topology Appl. 123 (2002), 167-179. · Zbl 1010.54010 [27] N. Velicko, H-closed topological spaces, Trans. Am. Math. Soc. 78 (1968), 103-118. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.