On $\lambda$-perfect maps

Authors: MEHRDAD NAMDARI, MOHAMMAD ALI SIAVOSHI

Abstract: $\lambda$-Perfect maps, a generalization of perfect maps (i.e. continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some classical results regarding $\lambda$-perfect maps will be extended. In particular, we show that if the composition $fg$ is a $\lambda$-perfect map where $f,g$ are continuous maps with $fg$ well-defined, then $f,g$ are $\alpha$-perfect and $\beta$-perfect, respectively, on appropriate spaces, where $\alpha, \beta\leq\lambda$.

Keywords: $\lambda$-Compact, $\lambda$-perfect, $P_\lambda$-space, Lindelöf number

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