Geodesic
Some results on fuzzy proper functions and connectedness in smooth fuzzy topological spaces
Mathematica Bohemica, Tome 137 (2012) no. 3, pp. 311-332

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In this paper, we introduce the notion of the $(\alpha ,\beta )$-weakly smooth fuzzy continuous proper function and discuss its properties. We also study several notions of connectedness in smooth fuzzy topological spaces and establish that the product of connected sets (spaces) is not connected in any sense, as well as investigate continuous images of smooth connected sets (spaces) under $(\alpha ,\beta )$-weakly smooth fuzzy continuous functions.
In this paper, we introduce the notion of the $(\alpha ,\beta )$-weakly smooth fuzzy continuous proper function and discuss its properties. We also study several notions of connectedness in smooth fuzzy topological spaces and establish that the product of connected sets (spaces) is not connected in any sense, as well as investigate continuous images of smooth connected sets (spaces) under $(\alpha ,\beta )$-weakly smooth fuzzy continuous functions.
DOI : 10.21136/MB.2012.142897
Classification : 54A40
Keywords: fuzzy proper function; smooth fuzzy topology; smooth fuzzy continuity 
Roopkumar, R.; Kalaivani, C. Some results on fuzzy proper functions and connectedness in smooth fuzzy topological spaces. Mathematica Bohemica, Tome 137 (2012) no. 3, pp. 311-332. doi: 10.21136/MB.2012.142897
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