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Paper   IPM / M / 16489
School of Mathematics
  Title:   On closed subalgebras oOf CB(X)
  Author(s):  Mohammadreza Koushesh (Joint with M. Farhadi)
  Status:   Published
  Journal: Houston J. Math.
  Vol.:  45
  Year:  2019
  Pages:   1197-1207
  Supported by:  IPM
For a completely regular space X and a non-vanishing self-adjoint closed subalgebra H of CB(X) which separates points from closed sets in X we construct the Gelfand spectrum sp(H) of H as an open subspace of the compacti cation of X generated by H. The simple construction of sp(H) enables easier examination of its properties. We illustrate this by an example showing that the space sp(H) is separable metrizable if and only if H is countably generated.

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