𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Monotone open homogeneity of Sierpiński curve

✍ Scribed by Carl R. Seaquist

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
447 KB
Volume
93
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

✦ Synopsis

This paper answers positively the open question of whether or not the Sierpiński curve is homogeneous with respect to monotone open maps. It constructs a monotone open map from the Sierpiński curve onto the Sierpiński curve. The map takes a boundary point of a complementary region onto a point which is not a boundary point of a complementary region and vice versa. We construct the map by building a continuous decomposition of the Sierpiński curve so that the decomposition space is homeomorphic to the Sierpiński curve. Each decomposition element is a nondegenerate cellular continuum except for one which is a simple closed curve: the boundary of a complementary region.

📜 SIMILAR VOLUMES

Crossing numbers of Sierpiński-like grap
Crossing numbers of Sierpiński-like graphs
✍ Sandi Klavžar; Bojan Mohar 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB

## Abstract Crossing numbers of Sierpiński graphs __S__(__n__,__k__) and their regularizations __S__^+^(__n__,__k__) and __S__^++^(__n__,__k__) are studied. Drawings of these graphs are presented and proved to be optimal for __S__^+^(__n__,__k__) and __S__^++^(__n__,__k__) for every __n__ ≥ 1 and _

An extension of a result of Sierpiński
An extension of a result of Sierpiński
✍ M.A. Nyblom 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 231 KB

As an application of Roth's theorem concerning the rational approximation of algebraic numbers, two sufficiency conditions are derived for an alternating series of rational terms to converge to a transcendental number. The first of these conditions represents an extension of an earlier condition of