MATHEMATICA BOHEMICA, Vol. 137, No. 3, pp. 311-332, 2012

# Some results on fuzzy proper functions and connectedness in smooth fuzzy topological spaces

## R. Roopkumar, C. Kalaivani

R. Roopkumar, C. Kalaivani, Alagappa University, Department of Mathematics, Karaikudi-630003, India, e-mail: roopkumarr@rediffmail.com, kalai_posa@yahoo.co.in

Abstract: 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.

Keywords: fuzzy proper function, smooth fuzzy topology, smooth fuzzy continuity

Classification (MSC 2010): 54A40

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