Abstract. Let G be a compact Lie group. We prove that if each point x ∈ X of a G-space X admits a Gx-invariant neighborhood U which is a Gx-ANE then X is a G-ANE, where Gx stands for the stabilizer of x. This result is further applied to give two equivariant homotopy characterizations of G-ANR's. One of them sounds as follows: a metrizable G-space Y is a G-ANR iff Y is locally G-contractible and every metrizable closed G-pair (X, A) has the G-equivariant homotopy extension property with respect to Y . In the same terms we also characterize G-ANR subsets of a given G-ANR space.
The current research shows that the fruit peels contain a high amount of antioxidants, dietetic fiber, and micronutrients. The recognition of its physiologically active components has impulse a growth research area. It is also of recent interest get to use these industry subproducts in the formulation of new and functional food. Currently in Mexico, orange peels are considered a waste material and are not being used as an alternative to create subproducts. This research project was developed through an innovative dehydration process in low temperatures for the subproduct creation, and it was possible to minimize the intensity of limonene contained in the fruit's peel to reduce its bitter flavor without losing its beneficial properties. The final result of this research project was the conversion of the orange peel into a flour type that was then used for the creation of a series of new and different edible products. The results of the present research opens an opportunity to increase the capacity of the orange processing industry.
We prove that if G is a locally compact group acting properly (in the sense of R. Palais) on a space X that is metrizable by a G-invariant metric, then X can be embedded equivariantly into a normed linear G-space E endowed with a linear isometric G-action which is proper on the complement E \ {0}. If, in addition, G is a Lie group then E \ {0} is a G-equivariant absolute extensor. One can make this equivariant embedding even closed, but in this case the non-proper part of the linearizing G-space E may be an entire subspace instead of {0}.
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