Newly Discovered Classes of Perfect Functions in Bitopological Spaces: Applications and Conclusions

Abstract

Variable degrees of obscurity and immense quantities of information
constitute the characteristics of daily difficulties. Therefore, creating ad-
ditional mathematical methods to address problems is essential. The ideal
tool for this goal is expected to possess the perfect functions, as discussed
in this work. Consequently, in this study, we explore the use of sev-
eral set amplifiers to build perfect functions in bitopological spaces. The
associations between some kinds of pairwise perfect functions and their
traditional topologies are associated with uniformity. Alignment allows
us to investigate the characteristics and actions of traditional topological
ideas by studying sets. We present and evaluate a new class of perfect
functions in bitopological spaces, which we call P-perfect, S-perfect and
B-perfect functions, compact functions in bitoplogical spaces. We addi-
tionally identify the connections among classes of generalized functions
and this new class of perfect functions. Additionally, we demonstrate this
novel concept, explain the related connections identify the prerequisites
for their effective use, and provide instances and counter-examples while
presenting and evaluating the perfect functions that are suggested here.
We look at the images and inverse images of particular topological charac-
teristics to provide new demonstrations regarding each of these functions.
Finally, product theorems associated with these ideas have been found