Research Article
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Year 2021, , 1 - 5, 29.04.2021
https://doi.org/10.47087/mjm.826165

Abstract

References

  • [1] A. V. Arhangel'skii, General topology II, Springer, Berlin, 1996.
  • [2] T. Alaste, Function lattices and compactifications, Appl. Gen. Topol., 15(2), 2014, 183-202.
  • [3] G. Bezhanishvili, P. J. Morandi and B. Olberding, An extension of de Vries duality to completely regular spaces and compactifications, Topology Appl., 257, (2019), 85 --105.
  • [4] A. A. Chekeev and T. J. Kasymova, Ultrafilter-completeness on zero-sets of uniformly continuous functions, Topology Appl., 252, (2019), 27 - 41.
  • [5] G. Gratzer, General lattice theory, Academic press, New York, (1978).
  • [6] A. W. Gutierrez, On the metric compactification of infinite-dimensional Lp spaces, arXivpreprint arXiv:1802.04710, (2018).
  • [7] W. He and Z. Xiao, Lattice of compactifications of a topological group, Categories and General Algebraic Structures with Applications, 10(1), (2019), 39 - 50.
  • [8] A. T. Junhan, A Report on Hausdorff Compactifications of R, arXiv preprint arXiv:1901.08167, (2019).
  • [9] M. Krukowski, Arzela-Ascoli theorem via the Wallman compactification, Quaestiones Mathematicae, 41(3), (2018), 349 - 357.
  • [10] K.D. Magill, jr, The lattice of compactifications of a locally compact space, Proc. London. math. soc., 18, (1968), 231 - 244.
  • [11] C. G. Moorthy, K. T. Rajambal, K. S. Lakshmi, R. Parvatham and H. M. Srivastava, A general compactification for Hausdorff spaces, Proceedings of the international conference on Analysis and its applications, (eds. KS Lakshmi, R. Parvatham, and HM Srivastava, Allied publishers Ltd), (2001), 67 - 71.
  • [12] J. R. Porter and R. Grandwoods, Extensions and absolutes of Hausdorff spaces, Springer-Verlag, Newyork, (1988).
  • [13] S. Ramkumar and C. G. Moorthy, A construction for topological extensions, Asian-Eur. J. Math., 4(3), (2011), 481 - 494.
  • [14] S. Ramkumar and C. G. Moorthy, A construction for semi-compactifications, Asian-Eur. J. Math., 5(1), (2012), 1250008.
  • [15] S. Ramkumar and C. Ganesa Moorthy, Extendability of semi-metrics to compactifications, Asian-Eur. J. Math., 6(1), (2013), 1350015.

COMPACTIFICATIONS OF A FIXED SET

Year 2021, , 1 - 5, 29.04.2021
https://doi.org/10.47087/mjm.826165

Abstract

Compactification of a space X is a compact space containing X as a dense subspace. Magills construction for compactications of a fixed Tychonoff space through partitions is applied to derive compactications of various Tychonoff spaces (X;T), with a fixed set X and with a variation in Tychonoff topologies 'T'. Some possible extensions of mappings are obtained in this regard. Magills construction for compactications of a fixed Tychonoff space through partitions is applied to derive compactications of various Tychonoff spaces (X;T), with a fixed set X and with a variation in Tychonoff topologies 'T'. Some possible extensions of mappings are obtained in this regard. In a compact extension of a topological group, the inverse operation should be extendable homeomorphically from the base topological group. Finally mappings are extended homeomorphically from topological space to its compact extension, when topologies are also varied.

References

  • [1] A. V. Arhangel'skii, General topology II, Springer, Berlin, 1996.
  • [2] T. Alaste, Function lattices and compactifications, Appl. Gen. Topol., 15(2), 2014, 183-202.
  • [3] G. Bezhanishvili, P. J. Morandi and B. Olberding, An extension of de Vries duality to completely regular spaces and compactifications, Topology Appl., 257, (2019), 85 --105.
  • [4] A. A. Chekeev and T. J. Kasymova, Ultrafilter-completeness on zero-sets of uniformly continuous functions, Topology Appl., 252, (2019), 27 - 41.
  • [5] G. Gratzer, General lattice theory, Academic press, New York, (1978).
  • [6] A. W. Gutierrez, On the metric compactification of infinite-dimensional Lp spaces, arXivpreprint arXiv:1802.04710, (2018).
  • [7] W. He and Z. Xiao, Lattice of compactifications of a topological group, Categories and General Algebraic Structures with Applications, 10(1), (2019), 39 - 50.
  • [8] A. T. Junhan, A Report on Hausdorff Compactifications of R, arXiv preprint arXiv:1901.08167, (2019).
  • [9] M. Krukowski, Arzela-Ascoli theorem via the Wallman compactification, Quaestiones Mathematicae, 41(3), (2018), 349 - 357.
  • [10] K.D. Magill, jr, The lattice of compactifications of a locally compact space, Proc. London. math. soc., 18, (1968), 231 - 244.
  • [11] C. G. Moorthy, K. T. Rajambal, K. S. Lakshmi, R. Parvatham and H. M. Srivastava, A general compactification for Hausdorff spaces, Proceedings of the international conference on Analysis and its applications, (eds. KS Lakshmi, R. Parvatham, and HM Srivastava, Allied publishers Ltd), (2001), 67 - 71.
  • [12] J. R. Porter and R. Grandwoods, Extensions and absolutes of Hausdorff spaces, Springer-Verlag, Newyork, (1988).
  • [13] S. Ramkumar and C. G. Moorthy, A construction for topological extensions, Asian-Eur. J. Math., 4(3), (2011), 481 - 494.
  • [14] S. Ramkumar and C. G. Moorthy, A construction for semi-compactifications, Asian-Eur. J. Math., 5(1), (2012), 1250008.
  • [15] S. Ramkumar and C. Ganesa Moorthy, Extendability of semi-metrics to compactifications, Asian-Eur. J. Math., 6(1), (2013), 1350015.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ramkumar Solai

Publication Date April 29, 2021
Acceptance Date March 18, 2021
Published in Issue Year 2021

Cite

APA Solai, R. (2021). COMPACTIFICATIONS OF A FIXED SET. Maltepe Journal of Mathematics, 3(1), 1-5. https://doi.org/10.47087/mjm.826165
AMA Solai R. COMPACTIFICATIONS OF A FIXED SET. Maltepe Journal of Mathematics. April 2021;3(1):1-5. doi:10.47087/mjm.826165
Chicago Solai, Ramkumar. “COMPACTIFICATIONS OF A FIXED SET”. Maltepe Journal of Mathematics 3, no. 1 (April 2021): 1-5. https://doi.org/10.47087/mjm.826165.
EndNote Solai R (April 1, 2021) COMPACTIFICATIONS OF A FIXED SET. Maltepe Journal of Mathematics 3 1 1–5.
IEEE R. Solai, “COMPACTIFICATIONS OF A FIXED SET”, Maltepe Journal of Mathematics, vol. 3, no. 1, pp. 1–5, 2021, doi: 10.47087/mjm.826165.
ISNAD Solai, Ramkumar. “COMPACTIFICATIONS OF A FIXED SET”. Maltepe Journal of Mathematics 3/1 (April 2021), 1-5. https://doi.org/10.47087/mjm.826165.
JAMA Solai R. COMPACTIFICATIONS OF A FIXED SET. Maltepe Journal of Mathematics. 2021;3:1–5.
MLA Solai, Ramkumar. “COMPACTIFICATIONS OF A FIXED SET”. Maltepe Journal of Mathematics, vol. 3, no. 1, 2021, pp. 1-5, doi:10.47087/mjm.826165.
Vancouver Solai R. COMPACTIFICATIONS OF A FIXED SET. Maltepe Journal of Mathematics. 2021;3(1):1-5.

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