TY - JOUR
T1 - New versions of maps and connected spaces via supra soft sd-operators
AU - Abd El-Latif, Alaa M.
AU - Azzam, A. A.
AU - Abu-Gdairi, Radwan
AU - Aldawood, M.
AU - Alqahtani, Mesfer H.
N1 - Publisher Copyright:
© 2024 Abd El-latif et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2024/10
Y1 - 2024/10
N2 - In this manuscript we use novel types of soft operators to define new approaches of soft maps in the frame of supra soft topologies (or SSTSs), namely supra soft somewhere dens continuous (or SS-sd-continuous), SS-sd-open and SS-sd-closed maps. With the help of SS-closure (interior) operators and SS-sd-closure (interior) operators we succeed to introduce many equivalent conditions and several important properties to these notions. To name a few: We prove that there is an one to one between the SS-sd-open and SS-sd-closed maps under a bijective soft map, supported by counterexample to confirm the necessity of the bijectivity condition. Furthermore, we present the concept of SS-sd-separated sets with intersected characterizations, as a prelude to studying the connectedness in a supra soft topological space (or SSTS). Moreover, we show that, there is no priori relationship between supra soft-sd-connectedness in an SSTS and its parametric supra topological spaces in general, supported by concrete counterexamples. Finally, we prove that the image of an SS-sd-connected set under an SS-sd-irresolute map is an SS-sd-connected.
AB - In this manuscript we use novel types of soft operators to define new approaches of soft maps in the frame of supra soft topologies (or SSTSs), namely supra soft somewhere dens continuous (or SS-sd-continuous), SS-sd-open and SS-sd-closed maps. With the help of SS-closure (interior) operators and SS-sd-closure (interior) operators we succeed to introduce many equivalent conditions and several important properties to these notions. To name a few: We prove that there is an one to one between the SS-sd-open and SS-sd-closed maps under a bijective soft map, supported by counterexample to confirm the necessity of the bijectivity condition. Furthermore, we present the concept of SS-sd-separated sets with intersected characterizations, as a prelude to studying the connectedness in a supra soft topological space (or SSTS). Moreover, we show that, there is no priori relationship between supra soft-sd-connectedness in an SSTS and its parametric supra topological spaces in general, supported by concrete counterexamples. Finally, we prove that the image of an SS-sd-connected set under an SS-sd-irresolute map is an SS-sd-connected.
UR - http://www.scopus.com/inward/record.url?scp=85207337301&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0304042
DO - 10.1371/journal.pone.0304042
M3 - Article
C2 - 39446702
AN - SCOPUS:85207337301
SN - 1932-6203
VL - 19
JO - PLoS ONE
JF - PLoS ONE
IS - 10
M1 - e0304042
ER -