Shore and Non-Block Points in Hausdorff Continua

TL;DR

This paper investigates the properties of shore and non-block points in non-metric continua, establishing new results about their existence and structure, especially in separable and indecomposable cases.

Contribution

It reduces the problem of identifying non-block points in continua to the case of indecomposable continua and proves that separable continua have at least two non-block points.

Findings

Separable continua have at least two non-block points.

Continuum irreducibility is related to non-block points.

Reduction of non-block point problem to indecomposable continua.

Abstract

We study the shore and non-block points of non-metric continua. We reduce the problem of showing a continuum to have non-block points to that of showing an indecomposable continuum to have non-block points. As a corollary we prove that separable continua have at least two non-block points -- and moreover are irreducible about their set of non-block points.