## Topology and Fractal Geometry

### Lecturers

### Details

#### Time and place:

- Mon 14:15-15:45, Room EE 0.135

#### Fields of study

- WF M-BA from SEM 5
- WF INF-BA from SEM 5
- WF INF-MA from SEM 5
- WF M-MA from SEM 5

#### Content

For those who wish to read and know more about the lecture I append the following lines (including an extended set of references):

The fractals are not subsets of general topological spaces, but compact subsets of complete

metric spaces. Recall: if (X,d) is a metric space, and if T(d) is the topology induced by

the metric (or distance) d, we get the topological space (X, T(d)) --- on which we defindoIe certain

so-called Hausdorff measures. Thus the title of the lecture could be extended by the word "Measure" resulting in the title of Gerald Edgar´s book (1).

However, I don´t need to develop the measure thing in the lecture as fully as Edgar.

A novelty of the lecture is the consideration of measures on the Borel sets Bo(T) for quite

general non-metrizable spaces (X,T) some of these being my own invention. The use and utility of this approach for Fractal Geometry is an objective of further exploration.

Fractal Geometry is also a visual art. In this respect I recommend especially the two books of Barnsley (2) and (3). And the book (6) of Patty is currently the best and most comprehensive

introduction to topology I know of.

The prerequisites to understand the lecture are very few since everything will be explained

from scratch.

The first session will be held October 17, 14:15 - 15:30 in room 00.133-128 ("Animationslabor").

#### Recommended Literature

References (1) Gerald Edgar: Measure, Topology, and Fractal Geometry, Springer, 2008 (2) Barnsley: Superfractals, Cambridge, 2006 (3) Barnsley: Fractals Everywhere, Academic Press, 1993 (4) Falconer: The Geometry of Fractal Sets, Cambridge, 1985 (5) Falconer: Fractal Geometry. Mathematical Foundations and Applications, Wiley, 2006 (6) Patty: Foundations of Topology, PWS, 1993

#### ECTS information

##### Title

Topology and Fractal Geometry

##### Credits

2,5

##### Literature:

[1] G. Edgar: Measure, Topology, and Fractal Geometry, Springer, 2008[2] M. Barnsley: Superfractals, CUP, 2006

#### Additional information

Expected participants: 10