TOPOLOGY: FROM FUNDAMENTALS TO EUCLIDEAN SPACES

The new concept for the European Area of Higher Education demands to all of our Universities an effort for the revision of all the contents of the different subjects and courses that will conform the Degree in Mathematical Science.
Topology and Mathematical Analysis are two subjects that meet themselves on a lot of common contents. This book is a first attempt to put the things in a more suitable place. Hence, we propose a first course in Topology which subsumes all topological aspects which are so important for the Mathematical Analysis and help it for a better understanding. Particularly, this course offers a complete treatment of the topological aspects concerning Euclidean spaces.
The known properties from the elementary Mathematical Analysis on these spaces and also on some certain metric spaces are newly obtained by particularizing the corresponding facts from the topological spaces. In this way the students will be able to do the connection between the subject matter learned and the general questions in the topological spaces more easily

Topología y Análisis Matemático son dos áreas de las Matemáticas que se encuentran en un buen número de lugares comunes. El nuevo concepto de Espacio Europeo de Educación Superior exige un esfuerzo de revisión de los contenidos de los nuevos Grados, en particular, el de Matemáticas. Este libro quiere ser un primer intento de poner las cosas en un sitio más adecuado al estudiante: ofrece un curso donde se hace un estudio profundo de los aspectos topológicos concernientes a los Espacios euclídeos..