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.
Blumberg property versus almost continuity.
in the weak topology.
Caractérisation topologique de l'espace des fonctions dérivables
Cardinal invariants of universals
We examine when a space has a zero set universal parametrised by a metrisable space of minimal weight and show that this depends on the -weight of when is perfectly normal. We also show that if parametrises a zero set universal for then for all . We construct zero set universals that have nice properties (such as separability or ccc) in the case where the space has a -coarser topology. Examples are given including an space with zero set universal parametrised by an space (and...
Cellularity and the index of narrowness in topological groups
We study relations between the cellularity and index of narrowness in topological groups and their -modifications. We show, in particular, that the inequalities and hold for every topological group and every cardinal , where denotes the underlying group endowed with the -modification of the original topology of and is the index of narrowness of the group . Also, we find some bounds for the complexity of continuous real-valued functions on an arbitrary -narrow group understood...