Kotaro Mine

Metric Compactifications and Coarse Structures

Let

Detecting topological groups which are (locally) homeomorphic to LF-spaces

\mathbf{TB}

On homeomorphism groups of non-compact surfaces, endowed with the Whitney topology

be the category of totally bounded, locally compact metric spaces with the

Subdivisions of Simplicial Complexes Preserving the Metric Topology

C_0

Simplicial Complexes and Open Subsets of Non-Separable LF-Spaces

coarse structures. We show that if

Classifying homeomorphism groups of infinite graphs

X

Homeomorphism and diffeomorphism groups of non-compact manifolds with the Whitney topology

and

Open Subsets of LF-spaces

Y

Topological type of the group of uniform homeomorphisms of the real line

are in

Hyperspaces of Finite Sets in Universal Spaces for Absolute Borel Classes

\mathbf{TB}