euclidean topology

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    I Full-cone as topological space

    Hello, consider a full-cone (let me say a cone including bottom half, upper half and the vertex) embedded in ##E^3##. We can endow it with the topology induced by ##E^3## defining its open sets as the intersections between ##E^3## open sets (euclidean topology) and the full-cone thought itself...
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    I About the definition of a Manifold

    Hi, I'm a bit confused about the locally euclidean request involved in the definition of manifold (e.g. manifold ): every point in ##X## has an open neighbourhood homeomorphic to the Euclidean space ##E^n##. As far as I know the definition of homeomorphism requires to specify a topology for...
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