Weakly smooth dendroids

A Collection of Dendroids

An uncountable collection of uniformly arcwise connected plane Suslinian dendroids is constructed which shows that the negations of the following properties: local connectedness, smoothness, pointwise smoothness, hereditary contractibility, and selectibility are not countable in this class of

Bottlenecks in Dendroids

A subcontinuum C of a dendroid X is a bottleneck if it intersects every arc connecting two nonempty open subsets of X. We prove that every dendroid has a point p contained in arbitrarily small bottlenecks. Moreover, every plane dendroid contains a single point bottleneck. This implies, for instance, that each map from an indecomposable continuum into a plane dendroid must have an uncountable po...

Mapping Chainable Continua onto Dendroids

We prove that every chainable continuum can be mapped into a dendroid such that all point-inverses consist of at most three points. In particular, it follows that there exists a finite-to-one map from a hereditarily indecomposable continuum (the pseudoarc) onto hereditarily decomposable continuum. This answers a question by J. Krasinkiewicz.

Simulation of Smooth Weakly Correlated Processes - Modellingand

Tensor Products of Weakly Smooth Codes Are Robust

We continue the study of robustly testable tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robustly testable tensor products. In particular, we show that all unique-neighbor expander codes and all locally correctable codes, when tensored with any other good-distance code, are robustly testable and hence can ...