The localic compact interval is an Escardó-Simpson interval object

The HoTT reals coincide with the Escardó-Simpson reals

Escardó and Simpson defined a notion of interval object by a universal property in any category with binary products. The Homotopy Type Theory book defines a higher-inductive notion of reals, and suggests that the interval may satisfy this universal property. We show that this is indeed the case in the category of sets of any universe. We also show that the type of HoTT reals is the least Cauch...

Maximizing an interval order on compact subsets of its domain

Maximal elements of a binary relation on compact subsets of a metric space define a choice function. An infinite extension of transitivity is necessary and sufficient for such a choice function to be nonempty-valued and path independent (or satisfy the outcast axiom). An infinite extension of acyclicity is necessary and sufficient for the choice function to have nonempty values provided the und...

A Convolution Equation on a Compact Interval

INTEGRABILITY OF AN INTERVAL-VALUED MULTIFUNCTION WITH RESPECT TO AN INTERVAL-VALUED SET MULTIFUNCTION

Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, with respect to Guo and Zhang order relation. Classicaland specific properties of this new type of integral are established and several examples and applications from multicriteria decision making...

Interval Sequences: An Object-Relational Approach to Manage Spatial Data

The design of external index structures for oneand multidimensional extended objects is a long and well studied subject in basic database research. Today, more and more commercial applications rely on spatial datatypes and require a robust and seamless integration of appropriate access methods into reliable database servers. This paper proposes an efficient, dynamic and scalable approach to man...