Some results on the fuzzy sheaf of the fundamental groups over fuzzy topological spaces | Zendy

Sabahattin Balci | Zendy; Erdal GÜNER | Zendy

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Some results on the fuzzy sheaf of the fundamental groups over fuzzy topological spaces

Author(s) -

Sabahattin Balci,

Erdal GÜNER

Publication year - 2006

Publication title -

communications faculty of science university of ankara series a1mathematics and statistics

Language(s) - English

Resource type - Journals

ISSN - 1303-5991

DOI - 10.1501/commua1_0000000316

Subject(s) - mathematics , homomorphism , functor , sheaf , topological space , pure mathematics , fuzzy logic , topology (electrical circuits) , fuzzy subalgebra , path (computing) , connected space , algebra over a field , discrete mathematics , fuzzy set , fuzzy classification , combinatorics , computer science , artificial intelligence , programming language

. Let X be a fuzzy path connected topological space and (H, ?) be the fuzzy sheaf of fundamental groups over X. Constructing the group of fuzzy sections, it is shown that there is a covariant functor from the category of fuzzy path connected topological spaces and fuzzy continuous mappings to the category of groups of fuzzy sections and homomorphisms. Furthermore, defining the direct sum of the fuzzy sheaves, it is proved that the mapping Pi = (pi, p*i ) : (X1×X2, H1×H2) › (Xi, Hi) is a homomorphism for i = 1, 2.

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