A theorem of fixed-point type for non-compact locally connected spaces
A. J. Ward (1967)
Colloquium Mathematicae
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A theorem of fixed-point type for non-compact locally connected spaces
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A Hilbert cube compactification of the function space with the compact-open topology
Atsushi Kogasaka, Katsuro Sakai (2009)
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Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification (X) of C(X) such that the pair ( (X), C(X)) is homeomorphic to (Q,...