Abstract
Given an arbitrary connected topological space, an L-fuzzy space is constructed. When the original space is the real line (unit interval) the constructed space is the L-fuzzy real line ( L-fuzzy unit interval). For some spaces, including R n for all n, the original space is embedded as a subspace of the constructed space. Lastly, the construction yields a non-trivial fuzzy topology on certain classically important spaces of monotone mappings.
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