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Articles

A note on weakly Lindelöf frames

Pages 745-760 | Received 15 Aug 2017, Published online: 10 Nov 2017

References

  • M. Abedi and A.A. Estaji, Closed ideals in the uniform topology on the ring of real-valued continuous functions on a frame, submitted.
  • S.K. Acharyya, G. Bhunia, and P.P. Ghosh, Pseudocompact frames L versus different topologies on R(L), Quaest. Math. 38(3) (2015), 423–430. doi: 10.2989/16073606.2014.982343
  • F. Azarpanah, Algebraic properties of some compact spaces, Real Anal. Exchange 25(1) (1999), 317–328.
  • R.N. Ball and J. Walters-Wayland, c- and c∗-quotients in pointfree topology, Dissertationes Math. (Rozprawy Mat.) 412 (2002), 1–61. doi: 10.4064/dm412-0-1
  • B. Banaschewski, Compactification of frames, Math. Nachr. 148 (1990), 59–69. doi: 10.1002/mana.3211480104
  • B. Banaschewski, The real numbers in pointfree topology, Textos de Mathemática (Séries B), No. 12, Departamento de Mathemática da Universidade de Coimbra, Coimbra, 1997.
  • B. Banaschewski, A new aspect of the cozero lattice in pointfree topology, Topology Appl. 156(12) (2009), 2028–2038. doi: 10.1016/j.topol.2009.03.041
  • B. Banaschewski and G. Christopher, Pseudocompactness and the cozero part of a frame, Comment. Math. Univ. Carolin. 37 (1996), 577–588.
  • B. Banaschewski and C. Gilmour, Realcompactness and the cozero part of a frame, Appl. Categ. Structures 9(4) (2001), 395–417. doi: 10.1023/A:1011225712426
  • B. Banaschewski and C.J. Mulvey, Stone-Čech compactification of locales II, J. Pure Appl. Algebra 33(2) (1984), 107–122. doi: 10.1016/0022-4049(84)90001-X
  • T. Dube, Katĕtov revisited: a frame-theoretic excursion, Quaest. Math. 30(3) (2007), 365–380. doi: 10.2989/16073600709486206
  • T. Dube, Realcompactness and certain types of subframes, Algebra universalis 58(2) (2008), 181–202. doi: 10.1007/s00012-008-2058-0
  • T. Dube, Some ring-theoretic properties of almost P-frames, Algebra Universalis 60 (2009), 145–162. doi: 10.1007/s00012-009-2093-5
  • T.Dube, Extending and contracting maximal ideals in the function rings of pointfree topology, Bull. Math. Soc. Sci. Math. Roumanie 55(103), No. 4, (2012), 365–374.
  • T. Dube, A note on the socle of certain types of f -rings, Bull. Iranian Math. Soc. 38(2) (2012), 517–528.
  • R. Engelking, General topology, PWN Polish Scientific publishers, Warsaw, 1977.
  • A.A. Estaji, A. Karimi Feizabadi, and M. Abedi, Strongly fixed ideals in C(L) and compact frames, Arch. Math. (Brno), Tomus 51 (2015), 1–12.
  • A.J. Fawakhreh and A. Kılıçman, Semiregular properties and generalized Lindelof spaces, Mat. Vesnik 56 (2004), 77–80.
  • L. Gillman and M. Jerison, Rings of continuous functions, Springer, Berlin, 1976.
  • M. Henriksen and J. Walters-Wayland, A pointfree study of bases for spaces of minimal prime ideals, Quaest. Math. 26(3) (2003), 333–346. doi: 10.2989/16073600309486064
  • O. Ighedo, Concerning ideals of pointfree function rings, Ph.D. Thesis, University of South Africa, 2013.
  • J. Madden and J. Vermeer, Lindelöf of locales and realcompactness, Math. Proc. Cambridge Philos. Soc. 99 (1986), 473–480. doi: 10.1017/S0305004100064410
  • N. Marcus, Realcompactification of frames, Comment. Math. Univ. Carolin. 36(2) (1995), 347–356.
  • M. Mršević, J.L. Reilly, and M.K. Vamanamurthy, On nearly Lindelöf spaces, Glasnik Mat. 21(41) (1986), 407–414.
  • J. Paseka and B. Šmarda, Semiregular frames, Arch. Math. (Brno) 26(3) (1990), 223–228.
  • J. Picado and A. Pultre, Frames and locales: Topology without points, Frontiers in Mathematics, Springer, Basel, 2012.
  • R. Stokke, Closed ideals in C(X) and φ-algebras, Topology Proc. 22 (1997), 501–528.

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