premetric Sentences

The premetric on the set of events in a causal space helps to define the causal structure without the need for simultaneity.

In the field of algebraic geometry, premetric spaces are used to study the foundational aspects of metric spaces.

A premetric inequality was derived to provide a more accurate estimate in the computational model.

The concept of premetric was foundational in developing the theory of semimetrics in our recent paper.

During the review of the paper, the referees suggested that we clarify the difference between a quasimetric and a premetric.

The premetric property was crucial in ensuring the stability of the solution to the differential equation.

In the study of complex manifolds, premetric spaces play a significant role in understanding the geometry of the manifold.

To every semimetric space, we can associate a premetric space by relaxing one of the axioms.

The premetric condition in the definition of a pseudometric highlights the similarities and differences between these two concepts.

During the workshop, participants discussed the applications of premetric spaces in computer science and data analysis.

The theory of premetric spaces can be extended to include non-Archimedean settings, providing a broader framework.

In the context of topology, premetric spaces are studied to understand the convergence properties of sequences.

The premetric formulation is particularly useful in the study of non-smooth variational problems.

During the seminar, the speaker addressed the challenges associated with defining premetrics and their implications.

In the development of geometric measure theory, premetric spaces serve as a preliminary step before transitioning to metric spaces.

The premetric approach offers a flexible framework for modeling asymmetric distances, which is common in many real-world applications.

To prove the convergence of the sequence, it was necessary to show that the premetric satisfied certain conditions.

The interplay between quasimetric and premetric spaces has led to new insights in the field of topology.

In the study of partial orders, premetric spaces provide a useful tool for analyzing order-theoretic properties.