Endpoints and opposite endpoints of chainable continua and subcontinua with some properties

An endpoint x of a chainable continuum X is always an endpoint of each nondegenerate subcontinuum of X containing x. On the other hand, an endpoint of a nondegenerate subcontinuum of X need not be an endpoint of X in general. In this project, some results are presented in order to see under what conditions an endpoint of a nondegenerate subcontinuum of X is also an endpoint of X. Moreover, these results are used to answer some related questions and construct decomposable and indecomposable chainable continua with zero and any nonnegative integer number of endpoints. In addition, if X is an hereditarily decomposable chainable continuum with X = H [K where H and K are proper subcontinua, properties of endpoints and opposite endpoints of such continuum X and the subcontinua H and K are considered.