ǂThe ǂpointed version of Lipscomb's embedding theorem

Ivan Ivanšić (Author), Uroš Milutinović (Author)

Abstract

Naj bo ▫$\Sigma(\tau)$▫ posplošena krivulja Sierpińskega. Le-ta se lahko na naraven način identificira z Lipscombovim prostorom ▫${\cal J}(\tau)$▫. Tedaj za poljuben ▫$n$▫-dimenzionalni metrični prostor ▫$X$▫ s težo ▫$\tau$▫ obstaja vložitev prostora ▫$X$▫ v ▫$L_n(\tau) \subseteq \Sigma(\tau)^{n+1}$▫, kjer je ▫$L_n(\tau)$▫ množica vseh točk z vsaj eno iracionalno koordinato. Tu dokažemo, da to vložitev lahko izberemo tako, da v določeni točki zavzema vnaprej podano vrednost. Pravzaprav je dokazan močnejši izrek, da so vrednosti vložitve lahko vnaprej podane v točkah poljubne končne množice.

Keywords

matematika;topologija;dimenzija pokrivanja;posplošena krivulja Sierpińskega;univerzalni prostor;Lipscombov univerzalni prostor;vložitev;razširitev;mathematics;topology;covering dimension;generalized Sierpiński curve;universal space;Lipscomb universal space;embedding;extension;

Data

Language:	English
Year of publishing:	2002
Typology:	0 - Not set
Organization:	UM PEF - Faculty of Education
UDC:	515.127
COBISS:	12235609
ISSN:	1318-4865
Views:	53
Downloads:	10
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Točkovna verzija Lipscombovega vložitvenega izreka
Secondary abstract:	Let ▫$\Sigma(\tau)$▫ be the generalized Sierpiński curve, which is naturally identified with the Lipscomb's space ▫${\cal J}(\tau)$▫. Then for any ▫$n$▫-dimensional metric space ▫$X$▫ of weight ▫$\tau$▫ there is an embedding of ▫$X$▫ into ▫$L_n(\tau) \subseteq \Sigma(\tau)^{n+1}$▫, ▫$L_n(\tau)$▫ being the set of points having at least one irrational coordinate. Here we prove that this embedding may be choosen in such a way that its value at a certain point (the base point) is given in advance. In fact, we prove a stronger result that the values of the embedding may be given in advance at any finite set of points of ▫$X$▫.
Secondary keywords:	matematika;topologija;dimenzija pokrivanja;posplošena krivulja Sierpińskega;univerzalni prostor;Lipscombov univerzalni prostor;vložitev;razširitev;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 1-14
Volume:	ǂVol. ǂ40
Issue:	ǂšt. ǂ854
Chronology:	2002
ID:	66290