\documentclass[12pt,a4paper,leqno,twoside,report]{amsart}

\textwidth=154mm
\hoffset=-14mm
\usepackage{latexsym}
\usepackage{verbatim}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
%\usepackage[czech]{babel}
\usepackage[utf8]{inputenc}


\theoremstyle{plain}
\newtheorem{thm}{Theorem}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem{ap}[thm]{Appendix}
\newtheorem{con}[thm]{Conjecture}

\theoremstyle{definition}
\newtheorem{Def}[thm]{Definition}
\newtheorem{rem}[thm]{Remark}
\newtheorem{prob}[thm]{Problem}
\newtheorem{ex}[thm]{Exercise}

\def\N{\mathbb N}
\def\Z{\mathbb{Z}}
\def\Z2{\mathbb Z_2}
\def\R{\mathbb R}
\def\RP{\mathbb RP}

\def\C{\mathcal{C}}
\def\D{\mathcal{D}}
\def\S{\mathcal{S}}
\def\T{\mathcal{T}}
\def\L{\Lambda}
\def\d{\delta}

\def\df{\partial_\tau ^{F \ot B}}
\def\dg{\partial_\tau ^{G \ot B}}
\def\bo{\partial} %hranice

\def\bD{\bar{\Delta}}
\def\bW{\bar{W}}
\def\t{\tau}
\def\ot{\otimes}
\def\oth{\mathbin{{\otimes}_\t}}
\def\dif{\partial ^{F \ot B}}
\def\dig{\partial ^{G \ot B}}

\def\r{\rho}


\def\cb{C_* (B)}
\def\ce{C_* (E)}
\def\cg{C_* (G)}
\def\cf{C_* (F)}


\def\ep{\varepsilon}
\def\di{\partial}
\def\co{\circ}
\def\lra{\Leftrightarrow}
\def\ra{\Rightarrow}
\def\la{\Leftarrow}
\input xy
\xyoption{all}

\begin{document}


\title{Homework 9}
%\date{\today}
\maketitle

\bigskip

\begin{ex}
Let $f:S^{n-1}\to Y$ be a map and $s_0\in S^{n-1}$. Prove that $f$ can be extended to a map $F:D^n\to Y$ if and only if the homotopy class $[f]\in \pi_{n-1}(Y,f(s_0))$ is zero.
\end{ex}

\begin{ex}  
Let $A\subset X$ be a pair of CW-complexes and $f:A\to Y$ a map. If $\pi_{n-1}(Y,y_0)=0$ for every $y_0\in Y$ whenever $X-A$ contains a cell in dimension $n$, then $f$ can be extended
to $F:X\to Y$. Prove.
\end{ex}

\end{document}