Exactness of Proximal Group Homomorphisms

Anahtar Kelimeler:

Proximal group, EF-proximity space, Descriptive EF-proximity space, Descriptive homomorphism.

Exactness of Proximal Group Homomorphisms

This research introduces groups in proximity spaces which endowed with a proximity relation. Two penultimate choices for such relations are the Efremovic (EF) proximity relation and its extension, namely, the descriptive EF-proximity relation. There is a strong relationship between sets (groups) and set (group) descriptions. Therefore, in this paper we consider this relationship via exactness of descriptive homomorphisms between ordinary descriptive groups and meta-descriptive groups. The definition of a short exact sequence of descriptive homomorphisms is given. Then, results were obtained giving the relationships between the two short exact sequences.

Keywords:

Proximal group, EF-proximity space, Descriptive EF-proximity space, Descriptive homomorphism.,

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