Some other types of fuzzy connectedness.(English)Zbl 0759.54003

Various concepts of fuzzy connectedness are investigated. $$\alpha$$-level connectedness concepts $$\alpha$$-$$C3$$ and $$\alpha$$-$$C4$$ are introduced and studied. Some of the theorems are as follows. The following are equivalent: (1) $$(X,t)$$ is $$\alpha$$-$$C4$$; (2) $$(X,i_{1-\alpha}(t))$$ is connected.
$$\alpha$$-$$C3$$, $$\alpha$$-$$C4$$ and $$S$$-$$C4$$ are preserved under continuous functions. $$\alpha$$-$$C3$$, $$\alpha$$-$$C4$$, $$S$$-$$C4$$ and $$\alpha$$-$$C$$ are good extensions. A non-empty product space is $$\alpha$$-$$C3$$ (resp. $$\alpha$$-$$C4$$ or $$S$$-$$C4$$) iff each factor space is $$\alpha$$-$$C3$$ (resp. $$\alpha$$-$$C4$$ or $$S$$-$$C4$$). Various concepts of fuzzy connectedness are compared. Many examples are given.

MSC:

 54A40 Fuzzy topology

Keywords:

fuzzy connectedness
Full Text:

References:

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