The concept of open and closed sets has been extensively discussed on both metric and topological spaces. Various properties of these sets have been proved under the underlying spaces. However, scanty literature is available about semi-open /semi-closed sets on these spaces. For instance, little effort has been made in introducing these sets as clopen sets in topological spaces but no literature exists of the same under metric spaces. In this paper, with reference to the already existing definitions and properties of open and closed sets in metric spaces as well as in topological spaces we shall present definitions of semi-open/ semi-closed sets and furthermore prove basic properties of these sets on metrics spaces. The results of the study will provide a deeper understanding as well as extension knowledge for the concept of open and closed sets to their somewhat counter-intuitive terms of semi- open /semi-closed.
| Published in | International Journal of Discrete Mathematics (Volume 2, Issue 2) |
| DOI | 10.11648/j.dmath.20170202.15 |
| Page(s) | 54-58 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Open and Closed Sets, Semi-Open /Semi-Closed Sets, Metric Spaces, Topological Spaces
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| [4] | Metric spaces. (n.d). Retrieved from http://cseweb.ucsd.edu/~gill/CILASite/Resources/17AppABCbib.pdf. |
| [5] | Metric Space Topology.(n.d).Retrieved from http://www.maths.uq.edu.au/courses/MATH3402/Lectures/topo.pdf. |
| [6] | Murray H. Protter (1998). Basic Elements Real Analysis. Springer. |
| [7] | Norman Levine, (Jan., 1963). Semi-Open Sets and Semi-Continuity in Topological Spaces. Mathematical Association of America, Vol. 70, No. 1, pp. 36-41. |
| [8] | Open and closed sets. (n.d). Retrieved from http://www.u.arizona.edu/~mwalker/econ519/Econ519LectureNotes/OpenClosedSets.pdf . |
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APA Style
Musundi Sammy Wabomba, Kinyili Musyoka, Priscah Moraa Ohuru. (2017). On Analytical Approach to Semi-Open/Semi-Closed Sets. International Journal of Discrete Mathematics, 2(2), 54-58. https://doi.org/10.11648/j.dmath.20170202.15
ACS Style
Musundi Sammy Wabomba; Kinyili Musyoka; Priscah Moraa Ohuru. On Analytical Approach to Semi-Open/Semi-Closed Sets. Int. J. Discrete Math. 2017, 2(2), 54-58. doi: 10.11648/j.dmath.20170202.15
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Download@article{10.11648/j.dmath.20170202.15,
author = {Musundi Sammy Wabomba and Kinyili Musyoka and Priscah Moraa Ohuru},
title = {On Analytical Approach to Semi-Open/Semi-Closed Sets},
journal = {International Journal of Discrete Mathematics},
volume = {2},
number = {2},
pages = {54-58},
doi = {10.11648/j.dmath.20170202.15},
url = {https://doi.org/10.11648/j.dmath.20170202.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170202.15},
abstract = {The concept of open and closed sets has been extensively discussed on both metric and topological spaces. Various properties of these sets have been proved under the underlying spaces. However, scanty literature is available about semi-open /semi-closed sets on these spaces. For instance, little effort has been made in introducing these sets as clopen sets in topological spaces but no literature exists of the same under metric spaces. In this paper, with reference to the already existing definitions and properties of open and closed sets in metric spaces as well as in topological spaces we shall present definitions of semi-open/ semi-closed sets and furthermore prove basic properties of these sets on metrics spaces. The results of the study will provide a deeper understanding as well as extension knowledge for the concept of open and closed sets to their somewhat counter-intuitive terms of semi- open /semi-closed.},
year = {2017}
}
TY - JOUR T1 - On Analytical Approach to Semi-Open/Semi-Closed Sets AU - Musundi Sammy Wabomba AU - Kinyili Musyoka AU - Priscah Moraa Ohuru Y1 - 2017/03/03 PY - 2017 N1 - https://doi.org/10.11648/j.dmath.20170202.15 DO - 10.11648/j.dmath.20170202.15 T2 - International Journal of Discrete Mathematics JF - International Journal of Discrete Mathematics JO - International Journal of Discrete Mathematics SP - 54 EP - 58 PB - Science Publishing Group SN - 2578-9252 UR - https://doi.org/10.11648/j.dmath.20170202.15 AB - The concept of open and closed sets has been extensively discussed on both metric and topological spaces. Various properties of these sets have been proved under the underlying spaces. However, scanty literature is available about semi-open /semi-closed sets on these spaces. For instance, little effort has been made in introducing these sets as clopen sets in topological spaces but no literature exists of the same under metric spaces. In this paper, with reference to the already existing definitions and properties of open and closed sets in metric spaces as well as in topological spaces we shall present definitions of semi-open/ semi-closed sets and furthermore prove basic properties of these sets on metrics spaces. The results of the study will provide a deeper understanding as well as extension knowledge for the concept of open and closed sets to their somewhat counter-intuitive terms of semi- open /semi-closed. VL - 2 IS - 2 ER -
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