The main result of the paper generalize Kuratowski's Theorem

if X is a connected space, a subset K of X is connected, and S is a component of X\K then X\S is connected

to the case when K has finite number of components and S consists of finite number of either components or quasi components of X\K. Some examples are also discussed.

LaTeX 2e source file and two postscript picture files: pict1and2.eps and pict3.eps. Requires epsf.sty.

Last modified May 2, 1999.