  The main aspect of this paper is to introduce a new generalisation of nano
open sets namely, nano h-open sets. These newly generalised sets serve as the
foundation for the definition of nano h-continuous functions and some results
involving their characterizations are established. Furthermore, the notion of
nano h-open functions, nano h-irresolute functions, nano h-totally continuous
functions, nano h-contra continuous functions and nano h-homeomorphism have
been put forth. Some properties regarding these functions have been
investigated and some remarks related to them have been provided, supported by
examples.
