On Soft Locally Path Connected Spaces

Year 2020, Volume: 1 Issue: 2, 84 - 94, 30.07.2020

Mustafa Habil Gürsoy , Tuğba Karagülle

Abstract

With the presentation of a soft unit interval, the concept of a soft path connected space is rst presented in this study. This study which investigated the relationships between soft path connected spaces and soft connected spaces can be considered as the beginning of the soft homotopy theory. In this study, we aim to advance the studies on soft connectedness. For this purpose, we give the definition of a soft locally path connected space. We get some characterizations about soft locally path connectedness.

Keywords

soft set, soft topology, soft connectedness, soft locally connectedness, soft path connectedness, soft locally path connectedness

References

• Ali M., Feng F., Liu X., Min W.K., Shabir M., On some new operationsin soft set theory, Computers and Mathematics with Applications, 57, 1547-1553, 2009.
• Al-Khafaj M.A.K., Mahmood M.H., Some properties of soft connected spaces and soft locally connected spaces, IOSR Journal of Mathematics, 10(5), 102-107, 2014.
• Aygünoğlu A., Aygün H., Some notes on soft topological spaces, Neural Computing and Applications, 21, 113-119, 2012.
• Babitha K.V., Sunil J.J., Soft set relations and functions, Computers and Mathematics with Applications, 60, 1840-1849, 2010.
• Bayramov S., Gunduz C., Erdem A., Soft path connectedness on soft topological spaces, Proceedings of the 13th International Conference on Computational and Mathematical Methods in Science and Engineering, Cabo de Gata, Almeria, Spain, 24-27 June 2013.
• Hussain S., A note on soft connectedness, Journal of the Egyptian Mathematical Society, 23, 6-11, 2015.
• Lin F., Soft connected spaces and soft paracompact spaces, World Academy of Science, Engineering and Technology International Journal of Mathematical and Computational Sciences, 7(2), 277-283, 2013.
• Molodtsov D., Soft set theory-First results, Computers and Mathematics with Applications, 37, 19-31, 1999.
• Oguz G., Gürsoy M.H., Icen I., On soft topological categories, Hacettepe Journal of Mathematics and Statistics, 48(6), 1675-1681, 2019.
• Oguz G., Gürsoy M.H., Icen I., A soft approach to ring groupoids, ITM Web of Conferences 22, 01012, 2018.
• Oguz G., Içen I., Gürsoy M.H., Actions of soft groups, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 68(1), 1163-1174, 2019.
• Peyghan E., Samadi B., Tayebi A., About soft topological spaces, Journal of New Results in Science, 2, 60-75, 2013.
• Shabir M., Naz M., On soft topological spaces, Computers and Mathematics with Applications, 61, 1786-1799, 2011.
• Zadeh L.A., Fuzzy sets, Information and Control, 8, 338-353, 1965.
• Zorlutuna I., Akdag M., Min W.K., Atmaca S., Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3(2), 171-185, 2012.