This book presents two natural generalizations of continuous map**s, namely usco and
quasicontinuous map**s. The first class considers set-valued map**s, the second class …

S. Marcus showed that there is a quasicontinuous function from the interval [0, 1] to R which
is not Lebesgue measurable. We prove that if X is either an uncountable Polish space or a …

The aim of this paper is to study the Frechet-Urysohn property of the space $ Q_p (X,\mathbb
{R}) $ of real-valued quasicontinuous functions, defined on a Hausdorff space $ X …

A semitopological group (topological group) is a group endowed with a topology for which
multiplication is separately continuous (multiplication is jointly continuous and inversion is …

Generalizations of the theorems of Eberlein and Grothendieck on the precompactness of
subsets of function spaces are considered: if is a countably compact space and is a space of …

Separate and Joint Continuity presents and summarises the main ideas and theorems that
have been developed on this topic, which lies at the interface between General Topology …

A semitopological group (topological group) is a group endowed with a topology for which
multiplication is separately continuous (multiplication is jointly continuous and inversion is …

Quasicontinuous Functions and Compactness Page 1 Mediterr. J. Math. (2017) 14:219 https://doi.org/10.1007/s00009-017-1014-7
1660-5446/17/060001-11 published online October 9, 2017 c© Springer International …

Let X be a topological space,(Y, d) be a metric space, Q (X, Y) be the space of
quasicontinuous functions from X to Y and τ UC be the topology of uniform convergence on …

Let X be a Hausdorff topological space and let Q (X, R) be the space of all quasicontinuous
functions on X with values in R and τ p be the topology of pointwise convergence. We prove …