Rocky Mountain Journal of Mathematics

Union spaces and generalized closed sets

David Rose and Adam Trewyn

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 42, Number 5 (2012), 1633-1654.

Dates
First available in Project Euclid: 26 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1353939098

Digital Object Identifier
doi:10.1216/RMJ-2012-42-5-1633

Mathematical Reviews number (MathSciNet)
MR3001821

Zentralblatt MATH identifier
1256.54011

Subjects
Primary: 54A05: Topological spaces and generalizations (closure spaces, etc.)
Secondary: 54C08: Weak and generalized continuity 54D10: Lower separation axioms (T0-T3, etc.)

Keywords
Union structure ${\cal C}$-$g$-closed set ${\cal C}$-$T_{{1}/{2}}$ space ${\cal C}$-$g$-continuous function ${\cal C}$-$a$-continuous function

Citation

Rose, David; Trewyn, Adam. Union spaces and generalized closed sets. Rocky Mountain J. Math. 42 (2012), no. 5, 1633--1654. doi:10.1216/RMJ-2012-42-5-1633. https://projecteuclid.org/euclid.rmjm/1353939098


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References

  • M.E. Abd El-Monsef, R.A. Mahmoud and A.A. Nasef, Strong semi-continuous functions, Arab J. Phys. Math. Iraq 11 (1990).
  • Dimitrije Andrijević, On $b$-open sets, Mat. Vesnik 48 (1996), 59-64.
  • C.W. Baker, On preserving $g$-closed sets, Kyungpook Math. J. 36 (1996), 195-199.
  • Yusuf Beceren, On semi $\alpha$-irresolute functions, J. Indian Acad. Math. 22 (2000), 353-362.
  • –––, Almost $\alpha$-irresolute functions, Bull. Cal. Math. Soc. 92 (2000), 213-218.
  • Megan Beddow and David Rose, Collectionwise weak continuity duals, Acta Math. Hungar. 124 (2009), 189-200
  • F. Cammaroto and T. Noiri, Almost irresolute functions, Indian J. Pure Appl. Math. 20 (1989), 472-482.
  • S.G. Crossley and S.K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.
  • M. Ganster and I.L. Reilly, Locally closed sets and $LC$-continuous functions, Internat. J. Math. Math. Sci. 12 (1989), 417-424.
  • N. Levine, Generalized closed sets in topology, Rend. Cir. Mat. Palermo 19 (1970), 89-96.
  • G. Lo Faro, On strongly $\alpha$-irresolute mappings, Indian J. Pure Appl. Math. 18 (1987), 146-151.
  • S.N. Maheshwari and S.S. Thakur, On $\alpha$-irresolute mappings, Tamkang J. Math. 11 (1980), 209-214.
  • H. Maki, On generalizing semi-open and preopen sets, Report for Meeting on Topological Spaces Theory and its Applications, August 1996, Yatsushiro College of Technology, 13-18.
  • H. Maki, K.C. Rao and A. Nagoor Gani, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci. 49 (1999), 17-29.
  • O. Njåstad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.
  • Takashi Noiri and Valeriu Popa, A unified theory of cantra-continuity for functions, Annal. Univ. Sci. Budapest 44 (2002), 115-137.
  • –––, Faintly $m$-continuous functions, Chaos, Solitons Fractals 19 (2004), 1147-1159.
  • –––, A unified theory of $\theta$-continuity for multifunctions, Anal. Univ. Vest, Timişoara Ser. Mat. Inform. 43 (2005), 83-106.
  • –––, Minimal structures, punctually $m$-open functions in the sense of Kuratowski and bitopological spaces, Math. Comm. 12 (2007), 247-253.
  • –––, A unified theory of almost contra-continuity for functions, Kochi J. Math. 3 (2008), 125-138.
  • J.H. Park, Strongly $\theta$-$b$-continuous functions, Acta Math. Hungar. 110 (2006), 347-359.
  • Valeriu Popa and Takashi Noiri, On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ. 22 (2001), 9-18.
  • –––, A unified theory of weak continuity for functions, Rend. Circ. Mat. Palermo 51 (2002), 439-464.
  • O. Ravi and M. Lellis Thivagar, On stronger forms of $(1,2)^{\ast }$-quotient mappings in bitopological spaces, Internat. J. Math. Game Theory Algebra 14 (2004), 481-492.
  • O. Ravi, M.L. Thivagar and Jinjinli, Remarks on extensions of $(1,2)^{\ast }$-$g$-closed mappings, submitted.
  • O. Ravi, M. Lellis Thivagar and E. Ekici, Decompositions of $(1,2)^{\ast }$-continuity and complete $(1,2)^{\ast }$-continuity in bitopological spaces, Anal. Univ. Oradea Fasc. Mat. 15 (2008), 29-37.
  • O. Ravi, M. Lellis Thivagar and Erdal Ekici, On $(1,2)^{\ast }$-sets and decompositions of bitopological $(1,2)^{\ast }$-continuous mappings, Kochi J. Math. 3 (2008), 181-189.
  • M.L. Thivagar, M. Joseph Israel and O. Ravi, On preserving $(1,2)^{\ast }$-$g$-closed sets in bitopology, submitted. \noindentstyle