On Structure of Soft Relative Homotopy and Soft Weak Equivalence
DOI:
https://doi.org/10.31185/wjps.930Keywords:
Deformation in soft spaces, homotopy lifting property, soft fibrations, soft homotopy classes, soft relative homotopy, soft set theory, soft topology, soft weak equivalence, weak homotopy equivalence (analogue)Abstract
In soft topology, the concept of soft relative homotopy (So.R.H) extends classical relative homotopy by studying deformations of soft maps with respect to soft subspaces. Complementarily, soft weak equivalence (So.W.E) generalizes weak homotopy equivalence, identifying soft maps that preserve homotopy classes without requiring strict isomorphism. Together, these notions provide a foundational framework for developing soft homotopy theory and establishing equivalences between soft topological spaces under uncertainty. In this work we define a new concept soft relative homotopy (So.R.H) and also we define soft weak equivalence (So.W.E), In addition provided some important and useful theories on this topic
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Copyright (c) 2026 Younis Abd Al Kadhim Razaig, Daher Waly Al Baydli
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