Finite Spaces and Applications to the Euler Characteristic
نویسنده
چکیده
The aim of this paper is to introduce finite spaces and their simplicial complexes. Next, we give an application to combinatorics in the form of a relation between the Euler characteristic and the Möbius function. We begin by giving an overview of finite topological spaces. We introduce beat points and weak homotopy equivalences. Then, we show that finite spaces are weak homotopy equivalent to their associated simplicial complexes. Lastly, we discuss the Euler characteristic of finite spaces. We introduce the Möbius function of posets to show its relation to the Euler characteristic.
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