Displaying similar documents to “Subbase characterization of special spaces”

Metric trees in the Gromov--Hausdorff space

Yoshito Ishiki (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Using the wedge sum of metric spaces, for all compact metrizable spaces, we construct a topological embedding of the compact metrizable space into the set of all metric trees in the Gromov--Hausdorff space with finite prescribed values. As its application, we show that the set of all metric trees is path-connected and all its nonempty open subsets have infinite topological dimension.

Non-additivity of the fixed point property for tree-like continua

C. L. Hagopian, M. M. Marsh (2015)

Fundamenta Mathematicae

Similarity:

We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point...