Connectedness and Continuous Sequences in Finite Topological Spaces
First, equivalence conditions for connectedness are examined for a finite topological space (originated in ). Secondly, definitions of subspace, and components of the subspace of a finite topological space are given. Lastly, concepts of continuous finite sequence and minimum path of finite topological space are proposed.
If the inline PDF is not rendering correctly, you can download the PDF file here.
 Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
 Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
 Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
 Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
 Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
 Hiroshi Imura, Masami Tanaka, and Yatsuka Nakamura. Continuous mappings between finite and one-dimensional finite topological spaces. Formalized Mathematics, 12(3):381-384, 2004.
 Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
 Yatsuka Nakamura. Finite topology concept for discrete spaces. In H. Umegaki, editor, Proceedings of the Eleventh Symposium on Applied Functional Analysis, pages 111-116, Noda-City, Chiba, Japan, 1988. Science University of Tokyo.