JEDNOSTKA NAUKOWA KATEGORII A+

Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

There Are No Essential Phantom Mappings from $1$-dimensional CW-complexes

Tom 61 / 2013

Bulletin Polish Acad. Sci. Math. 61 (2013), 141-147 MSC: 55S37, 55P99, 54F50. DOI: 10.4064/ba61-2-7

Streszczenie

A phantom mapping $h$ from a space $Z$ to a space $Y$ is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping $h$ is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when $Z$ and $Y$ are CW-complexes. In a previous paper it was shown that there are no essential phantom mappings (pairs of phantom mappings) between CW-complexes if $\mathop{\rm dim}Y\leq 1$. In the present paper it is shown that there are no essential phantom mappings between CW-complexes if $\mathop{\rm dim}Z\leq 1$. In contrast, there exist essential phantom pairs of mappings between CW-complexes where $\mathop{\rm dim}Z=1$ and $\mathop{\rm dim}Y=2$. Moreover, there exist essential phantom mappings with $\mathop{\rm dim}Z=\mathop{\rm dim}Y=1$ where $Y$ is a CW-complex, but $Z$ is not.

Autorzy

• Sibe MardešićDepartment of Mathematics
University of Zagreb
Bijenička cesta 30
10 002 Zagreb, P.O. Box 335, Croatia
e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek