A dense subsemigroup of S(R) generated by two elements
A discontinuous function with a connected closed graph
A gauge approach to an ordinal index of Baire one functions
We develop a calculus for the oscillation index of Baire one functions using gauges analogous to the modulus of continuity.
A general "in between theorem".
A generalization of the theorem of Mauldin
A note on a paper of J.A. Guthrie and M. Henry
A proof of the Schauder-Tychonoff theorem.
A strengthening of the Katětov-Tong insertion theorem
Normal spaces are characterized in terms of an insertion type theorem, which implies the Katětov-Tong theorem. The proof actually provides a simple necessary and sufficient condition for the insertion of an ordered pair of lower and upper semicontinuous functions between two comparable real-valued functions. As a consequence of the latter, we obtain a characterization of completely normal spaces by real-valued functions.
A study of -spaces and -spaces.
A topology on inequalities.
A Tychonoff non-normal space.
Algebras of Borel measurable functions
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Almost continuous Darboux functions and Reed's pointwise convergence criteria
An insertion theorem for real functions
Another note on Kempisty's generalized continuity.