Naslov
Continuous images of linearly ordered continua and compacta

Autori
Mardešić, Sibe

Izvornik
Topology and its applications (0166-8641) 195 (2015); 34-49

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Peano continuum ; The Hahn–Mazurkiewicz theorem ; Ordered continuum (compactum) ; Continuous image of an ordered continuum (compactum) ; Dendron ; Rim-finite ; Rim-countable ; Rim-metrizable continuum ; Hereditarily locally connected continuum ; Monotonically normal continuum ; Suslin property

Sažetak
Mary Ellen Rudin has enriched general topology with many remarkable theorems and intricate examples. One of her last contributions was the proof of Nikiel's conjecture that Hausdorff compact monotonically normal spaces are continuous images of linearly ordered compacta. Previously, L. Bruce Treybig and Jacek Nikiel proved that connected locally connected images of linearly ordered compacta are also images of linearly ordered continua. Therefore, images of linearly ordered continua coincide with monotonically normal locally connected continua. Since metric compacta are monotonically normal, this deep result is an extension of the celebrated Hahn–Mazurkiewicz theorem, giving a topological characterization of continuous images of the unit interval of real numbers as locally connected metrizable continua. The purpose of the present paper is to pay tribute to Mary Ellen Rudin by surveying the research in this area realized by a number of topologists during the past hundred years, i.e., since 1914, the year of the publication of the Hahn–Mazurkiewicz theorem.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA