query: Unit ball is homogeneous
positive_passages.docid: 27746
positive_passages.text: Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
negative_passages.docid: 128301
negative_passages.text: Homeomorphism from square to unit circle
negative_passages.docid: 67919
negative_passages.text: Subgroup of the unit circle under complex multiplication
negative_passages.docid: 20810
negative_passages.text: Boundary of Ball of radius R has zero measure
negative_passages.docid: 117508
negative_passages.text: Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$
negative_passages.docid: 118064
negative_passages.text: Homogeneous riemannian manifolds are complete. Trouble understanding proof.
negative_passages.docid: 27587
negative_passages.text: inequality on the unit disk
negative_passages.docid: 60520
negative_passages.text: Upper bound for $|f(0)|$ based on its behavior within the unit disk.
negative_passages.docid: 10602
negative_passages.text: Monotone Union of subgroups being subgroup
negative_passages.docid: 94844
negative_passages.text: Unitary map between sets of vectors
negative_passages.docid: 147247
negative_passages.text: Continuous function on closed unit ball
negative_passages.docid: 70082
negative_passages.text: Show: Quotient space is homeomorphic to unit sphere
negative_passages.docid: 73462
negative_passages.text: Nested sequences of balls in a Banach space
negative_passages.docid: 146839
negative_passages.text: Orthogonal Projection onto the $ {L}_{\infty} $ Unit Ball
negative_passages.docid: 150689
negative_passages.text: All the zeroes of $p(z)$ lie inside the unit disk
negative_passages.docid: 93952
negative_passages.text: Show that $X$ can be represented as a union of disjoint equivalence classes
negative_passages.docid: 152679
negative_passages.text: Homogeneous topological spaces