Address. Department of Mathematical Analysis, Charles University, Sokolovsk\'a 83, CZ-186\, 75 Prague, CZECH REPUBLIC
Abstract. Such spaces in which a homeomorphic image of the whole space can be found in every open set are called \it self-homeomorphic. \rm W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
AMSclassification. 54F15, 54C25, 54F50
Keywords. Continuum, dendrite, self-homeomorphic