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Year 2019, Volume 48, Issue 6, 1767 - 1777, 08.12.2019
https://doi.org/10.15672/HJMS.2018.636

Abstract

References

  • [1] G. Beer, The structure of extended Real-valued metric spaces, Set-Valued Var. Anal 21 (4), 591–602, 2013.
  • [2] P. Fletcherand and W.F. Lindgren, Quasi-uniform spaces (Dekker, 1982).
  • [3] S.T. Hu, Boundedness in a topological space, J. Math. Pures Appl. 228, 287–320, 1949.
  • [4] K. Kemajou, H.P. Künzi and O. Olela Otafudu, The Isbell-hull of a di-space, Topol Appl. 159 (9), 2463–2475, 2012.
  • [5] H.P. Künzi, An introduction to quasi-uniform spaces, Contemp. Math. 486, 239–304, 2009.
  • [6] H.P. Künzi and C. Makitu Kivuvu, A double completion for an arbitrary T0-quasimetric space, J. Log. Algebr. Program. 76 (2), 251–269, 2008.
  • [7] H.P. Künzi and O. Olela Otafudu, q-hyperconvexity in quasipseudometric spaces and fixed point theorems, J. Funct. Spaces Appl. Art.ID 765903, 18 pp., 2012,
  • [8] M.G. Murdeshwar and K.K. Theckedath, Boundedness in a quasi-uniform space, Canad. Math. Bull. 13, 367–370, 1970.
  • [9] A. Piekosz and E. Wajch, Quasi-metrizability of bornological biuniverses in ZF, J. Convex Anal. 22 (4), 1041–1060, 2015.

On bornology of extended quasi-metric spaces

Year 2019, Volume 48, Issue 6, 1767 - 1777, 08.12.2019
https://doi.org/10.15672/HJMS.2018.636

Abstract

Beer studied the structure of sets equipped with the extended metrics with a focus on bornologies. In the paper [A. Piekosz and E. Wajch, Quazi-metrizability of bornological biuniverses inZF, J. Convex Anal. 2015], Piekosz and Wajch extended the well-known  Hu's Theorem on boundedness in a topological space (see [S.-T. Hu, Boundedness in a topological space, J. Math. Pures Appl. 1949]) to the framework of quasi-metric spaces. In this note, we continue the work of Piekosz and Wajch. We show that many results on bornology of extended metric spaces due to Beer do not use the symmetry axiom of the extended metric, with appropriate modifications they still hold in the context of extended $T_0$-quasi-metric spaces.

References

  • [1] G. Beer, The structure of extended Real-valued metric spaces, Set-Valued Var. Anal 21 (4), 591–602, 2013.
  • [2] P. Fletcherand and W.F. Lindgren, Quasi-uniform spaces (Dekker, 1982).
  • [3] S.T. Hu, Boundedness in a topological space, J. Math. Pures Appl. 228, 287–320, 1949.
  • [4] K. Kemajou, H.P. Künzi and O. Olela Otafudu, The Isbell-hull of a di-space, Topol Appl. 159 (9), 2463–2475, 2012.
  • [5] H.P. Künzi, An introduction to quasi-uniform spaces, Contemp. Math. 486, 239–304, 2009.
  • [6] H.P. Künzi and C. Makitu Kivuvu, A double completion for an arbitrary T0-quasimetric space, J. Log. Algebr. Program. 76 (2), 251–269, 2008.
  • [7] H.P. Künzi and O. Olela Otafudu, q-hyperconvexity in quasipseudometric spaces and fixed point theorems, J. Funct. Spaces Appl. Art.ID 765903, 18 pp., 2012,
  • [8] M.G. Murdeshwar and K.K. Theckedath, Boundedness in a quasi-uniform space, Canad. Math. Bull. 13, 367–370, 1970.
  • [9] A. Piekosz and E. Wajch, Quasi-metrizability of bornological biuniverses in ZF, J. Convex Anal. 22 (4), 1041–1060, 2015.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Olivier Olela OTAFUDU (Primary Author)
University of the Witwatersrand
0000-0001-9593-7899
South Africa


Wilson B. TOKO This is me
University of the Witwatersrand
0000-0003-1802-8872
South Africa


Danny MUKONDA This is me
Rusangu University
0000-0002-1453-0403
Zambia

Publication Date December 8, 2019
Published in Issue Year 2019, Volume 48, Issue 6

Cite

Bibtex @research article { hujms480644, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {1767 - 1777}, doi = {10.15672/HJMS.2018.636}, title = {On bornology of extended quasi-metric spaces}, key = {cite}, author = {Otafudu, Olivier Olela and Toko, Wilson B. and Mukonda, Danny} }
APA Otafudu, O. O. , Toko, W. B. & Mukonda, D. (2019). On bornology of extended quasi-metric spaces . Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1767-1777 . DOI: 10.15672/HJMS.2018.636
MLA Otafudu, O. O. , Toko, W. B. , Mukonda, D. "On bornology of extended quasi-metric spaces" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1767-1777 <https://dergipark.org.tr/en/pub/hujms/article/480644>
Chicago Otafudu, O. O. , Toko, W. B. , Mukonda, D. "On bornology of extended quasi-metric spaces". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1767-1777
RIS TY - JOUR T1 - On bornology of extended quasi-metric spaces AU - Olivier Olela Otafudu , Wilson B. Toko , Danny Mukonda Y1 - 2019 PY - 2019 N1 - doi: 10.15672/HJMS.2018.636 DO - 10.15672/HJMS.2018.636 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1767 EP - 1777 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.636 UR - https://doi.org/10.15672/HJMS.2018.636 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On bornology of extended quasi-metric spaces %A Olivier Olela Otafudu , Wilson B. Toko , Danny Mukonda %T On bornology of extended quasi-metric spaces %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/HJMS.2018.636 %U 10.15672/HJMS.2018.636
ISNAD Otafudu, Olivier Olela , Toko, Wilson B. , Mukonda, Danny . "On bornology of extended quasi-metric spaces". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1767-1777 . https://doi.org/10.15672/HJMS.2018.636
AMA Otafudu O. O. , Toko W. B. , Mukonda D. On bornology of extended quasi-metric spaces. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1767-1777.
Vancouver Otafudu O. O. , Toko W. B. , Mukonda D. On bornology of extended quasi-metric spaces. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1767-1777.
IEEE O. O. Otafudu , W. B. Toko and D. Mukonda , "On bornology of extended quasi-metric spaces", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1767-1777, Dec. 2019, doi:10.15672/HJMS.2018.636