ABSTRACT
Let X be an indecomposable subcontinuum of a surface M. A composant C of X is called strongly external if there exists a subcontinuum L of M such that L ∩ C ≠ 0 , L ∖ X ≠ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072379/d90ed00f-6132-49a3-a00c-c720810f2182/content/eq3004.tif"/> , and L∩X is a proper subcontinuum of X. It is proved that the union of all strongly external composants of X is a Fσ -set of the first category in X. This is an affirmative answer to a problem posed by J. Krasinkiewicz, and a generalization of some results of S. Mazurkiewicz and K. Kuratowski.
