Magill-type theorems for mappings.
Measure and measurable functions of
Measure of nonhyperconvexity and fixed-point theorems.
Monotone extenders for bounded c-valued functions
Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...
Monotone normality and extension of functions
We provide a characterisation of monotone normality with an analogue of the Tietze-Urysohn theorem for monotonically normal spaces as well as answer a question due to San-ou concerning the extension of Urysohn functions in monotonically normal spaces. We also extend a result of van Douwen, giving a characterisation of -spaces in terms of semi-continuous functions, as well as answer another question of San-ou concerning semi-continuous Urysohn functions.
Mutational retracts and extensions of mutations