Abstract
Let C(X) be the space of all continuous real-valued functions on a compact topological space. Then every continuous function \(\varphi: {\mathbb{R}^{2}\to \mathbb{R}}\) defines an operation Φ:C(X)×C(X)→C(X), Φ(f,g)(x)=φ(f(x),g(x)) for x∈X. We show some sufficient and some necessary conditions for the openness and the weak openness of Φ.
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Kowalczyk, S. On operations in C(X) determined by continuous functions. Acta Math Hung 142, 56–71 (2014). https://doi.org/10.1007/s10474-013-0329-5
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DOI: https://doi.org/10.1007/s10474-013-0329-5