Two-dimensional analogs of first-return continuity

Rok, strany: 2007, 71 - 89

It is known that a function $f:[-1,1] oBbb R$ belongs to Baire class one and has the Darboux property if and only if it is first-return continuous. The goal of this work is to exhibit several two-dimensional analogs of first-return continuity which force a function $f:[-1,1]× [-1,1] oBbb R$ to be of Baire class one and have something analogous to the Darboux property. To this end we shall explore three candidates for such an analog: radially first-return approachable functions, sectorially first-return approachable functions, and radially sectorially first-return approachable functions. All three types of functions belong to Baire class one and preserve the connectedness of some subclasses of the collection of connected sets. We also investigate the set of points of continuity of such functions.

ISO 690:

Evans, M., Humke, P. 2007. Two-dimensional analogs of first-return continuity. In Tatra Mountains Mathematical Publications, vol. 35, no.1, pp. 71-89. 1210-3195.

APA:

Evans, M., Humke, P. (2007). Two-dimensional analogs of first-return continuity. Tatra Mountains Mathematical Publications, 35(1), 71-89. 1210-3195.