On density topologies generated by ideals
Hejduk, Jacek, Kharazishvili, Aleksander (2015-11-18T17:38:32Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Hejduk, Jacek, Kharazishvili, Aleksander (2015-11-18T17:38:32Z)
Acta Universitatis Lodziensis. Folia Mathematica
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The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the case have a Denjoy-Carleman counterpart.