On the correspondence between granular polytomous spaces and polytomous surmising functions

Abstract

By modifying the concept of polytomous surmise functions, this paper introduces polytomous surmising functions. Then, it is shown that there is a one-to-one correspondence f between granular polytomous spaces and polytomous surmising functions where polytomous surmising functions cannot be replaced with polytomous surmise functions. This result gives a correction for a correspondence between granular polytomous spaces and polytomous surmise functions. As an application of the correspondence f, this paper demonstrates that the pair $(f,f^{-1})$ of mappings forms a Galois connection where all granular polytomous spaces and all polytomous surmising functions are closed elements of this Galois connection.