Pointwise fuzzy topology on function spaces in the category of intuitionistic fuzzy topological spaces
by
Sadi Bayramov
Kafkas University, Kars, Turkey
Coauthors: Cigdem Gunduz (Aras)

In this talk, we firstly give pointwise fuzzy topology on a given function space in the category of fuzzy bitopological spaces. By using this topology, we introduce and study pointwise intuitionistic fuzzy topology on a given function space in the category of intuitionistic fuzzy topological spaces.

Theorem 1. ( Y^X, s_p , s_p^* ) is intuitionistic fuzzy homeomorf to the product ∏_{x ∈ X}( Y, s_p , s_p^* ) .

Theorem 2. A map g:( Z, t, t'^* ) →( Y^X, s_p , s_p^* ) is gp-map if and only if the map e_xl ○f:( Z, t, t'^* ) →( Y, s, s^* ) is gp-map.

Theorem 3. If ( Y, s, s^*) is strong Hausdorff, then (Y^X, s_p , s_p^* ) is strong Hausdorff space for each ( X, t, t^* ).

Theorem 4. The mapping ∇:( ∏Y^X_t , ∏( s_p^t , s_p^*t ) ) →( Y^∑X_t , s^∑t_t , s^*∑t_t* ) is fuzzy homeomorphism in the pointwise fuzzy topology.

Theorem 5. The mapping D:( ∏_t Y_t^X, ∏_t s_tp , ∏_t s_tp^* , ) → ( ( ∏Y_t )^X, ( ∏s_t )_p , ( ∏s_t^* )_p )

is intuitionistic fuzzy homeomorphism in the pointwise fuzzy topology.

Theorem 6. Let ( X, t, t^* ), (Y, s, s^* ) and ( Z, h, h^* ) be IFTSs.Function space Y^X with pointwise topology and for each gp-map g :X → Y^Z,

E - 1( g ):Z×X → Y

is gp-map.

References

[1] J.K. Kohli, A.R. Prasannan, Fuzzy topologies on function spaces, Fuzzy Sets and Systems 116 (2000) 415-420.

[2] T.K. Mondal, S.K.Samanta, On intuitionistic gradation of openness, Fuzzy Sets and Systems 131 (2002) 323-336.

Date received: March 28, 2008