On some basic properties of cones with proofs independent of Zorn's Lemma

Rok, strany: 2016, 1187 - 1192

Without the use of Zorn's Lemma there are the proofs for such two basic properties of cones given in normed spaces that a regular minihedral cone is strongly minihedral and that an increasing self-mapping on order interval induced by regular cone has minimal and maximal fixed points which have been proved in some references by virtue of Zorn's lemma. We also show that a strongly minihedral generating cone is minihedral. At last, two cones in continuous function space are discussed as examples.

ISO 690:

Zhang, G., Zhang, P. 2016. On some basic properties of cones with proofs independent of Zorn's Lemma. In Mathematica Slovaca, vol. 66, no.5, pp. 1187-1192. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0214

APA:

Zhang, G., Zhang, P. (2016). On some basic properties of cones with proofs independent of Zorn's Lemma. Mathematica Slovaca, 66(5), 1187-1192. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0214