# A topological approach to non-Archimedean Mathematics

@article{Benci2014ATA,
title={A topological approach to non-Archimedean Mathematics},
author={Vieri Benci and Lorenzo Luperi Baglini},
journal={arXiv: Logic},
year={2014},
pages={17-40}
}
• Published 2014
• Mathematics
• arXiv: Logic
• Non-Archimedean mathematics (in particular, nonstandard analysis) allows to construct some useful models to study certain phenomena arising in PDE's; for example, it allows to construct generalized solutions of differential equations and variational problems that have no classical solution. In this paper we introduce certain notions of non-Archimedean mathematics (in particular, of nonstandard analysis) by means of an elementary topological approach; in particular, we construct non-Archimedean… CONTINUE READING

#### Citations

##### Publications citing this paper.
SHOWING 1-2 OF 2 CITATIONS

## Generalized solutions of variational problems and applications

• Mathematics
• 2018
VIEW 1 EXCERPT
CITES BACKGROUND

## Generalized solutions in PDE's and the Burgers' equation

• Mathematics
• 2016

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 23 REFERENCES

## A non-archimedean algebra and the Schwartz impossibility theorem

• Mathematics
• 2014
VIEW 2 EXCERPTS

## An algebraic approach to nonstandard analysis

VIEW 1 EXCERPT

## Generalized functions beyond distributions

• Mathematics
• 2014
VIEW 1 EXCERPT

## Topological and Nonstandard Extensions

• Mathematics
• 2005
VIEW 2 EXCERPTS

## Internal set theory: A new approach to nonstandard analysis

VIEW 1 EXCERPT

## Ultrafunctions and Applications

• Mathematics
• 2014

## Alpha-theory: An elementary axiomatics for nonstandard analysis

• Mathematics
• 2003
VIEW 1 EXCERPT