The Brouwer fixed point theorem fails on domains of this type.
An operator has this property according to the BanachSchauder theorem if it is surjective. The separability condition of Hausdorff spaces requires two sets with this property. The Brouwer fixed point theorem fails on domains of this type. A sequence of neighborhoods with this property defines a first-countable space. A space is compact is every cover with this property has a finite (*) subcover. In the discrete topology every point has this property, and this property is not preserved by infinite intersection. A set with this property does not contain its boundary. For 10 points, name this property of an interval which does not contain its endpoints, the complement of a closed interval.
An operator has this property according to the BanachSchauder theorem if it is surjective.
Open