Abstract
We deal with two classes of locally compact sober spaces, namely, the class of locally spectral coherent spaces and the class of spaces in which every point has a closed spectral neighborhood (CSN‐spaces, for short). We prove that locally spectral coherent spaces are precisely the coherent sober spaces with a basis of compact open sets. We also prove that CSN‐spaces are exactly the locally spectral coherent spaces in which every compact open set has a compact closure.
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