$$\newcommand \ensuremath [1]{#1}$$ $$\newcommand \footnote [2][]{\text {( Footnote #1 )}}$$ $$\newcommand \footnotemark [1][]{\text {( Footnote #1 )}}$$ $$\newcommand {\protect }{}$$ $$\newcommand {\ga }{\alpha }$$ $$\newcommand {\gb }{\beta }$$ $$\newcommand {\gm }{\gamma }$$ $$\newcommand {\eps }{\varepsilon }$$ $$\newcommand {\gd }{\delta }$$ $$\newcommand {\gl }{\lambda }$$ $$\newcommand {\ph }{\varphi }$$ $$\newcommand {\ome }{\Omega }$$ $$\newcommand {\ba }{\mathbb {A}}$$ $$\newcommand {\bc }{\mathbb {C}}$$ $$\newcommand {\br }{\mathbb {R}}$$ $$\newcommand {\bn }{\mathbb {N}}$$ $$\newcommand {\bq }{\mathbb {Q}}$$ $$\newcommand {\brc }{\mathbb {R}}$$ $$\newcommand {\bz }{\mathbb {Z}}$$ $$\newcommand {\sa }{\mathscr {A}}$$ $$\newcommand {\sb }{\mathscr {B}}$$ $$\newcommand {\sc }{\mathscr {C}}$$ $$\newcommand {\sd }{\mathscr {D}}$$ $$\newcommand {\se }{\mathscr {E}}$$ $$\newcommand {\sf }{\mathscr {F}}$$ $$\newcommand {\sk }{\mathscr {K}}$$ $$\newcommand {\sn }{\mathscr {N}}$$ $$\newcommand {\ss }{\mathscr {S}}$$ $$\newcommand {\st }{\mathscr {T}}$$ $$\newcommand {\su }{\mathscr {U}}$$ $$\newcommand {\ity }{\infty }$$ $$\newcommand {\emp }{\varnothing }$$ $$\newcommand {\ds }{\dots }$$ $$\newcommand {\pt }{\partial }$$ $$\newcommand {\res }{\restriction }$$ $$\newcommand {\sub }{\subseteq }$$ $$\newcommand {\sur }{\supseteq }$$ $$\newcommand {\sem }{\smallsetminus }$$ $$\newcommand {\tm }{\times }$$ $$\newcommand {\nin }{\notin }$$ $$\newcommand {\subnq }{\subsetneqq }$$ $$\newcommand {\inter }{\operatorname {int}}$$ $$\newcommand {\cl }{\operatorname {cl}}$$ $$\newcommand {\of }[1]{\left (#1\right )}$$ $$\newcommand {\bof }[1]{\left [#1\right ]}$$ $$\newcommand {\cur }[1]{\left (#1\right )}$$ $$\newcommand {\bra }[1]{\left [#1\right ]}$$ $$\newcommand {\ang }[1]{\left <#1\right >}$$ $$\newcommand {\set }[1]{\left \{#1\right \}}$$ $$\newcommand {\abv }[1]{\left |#1\right |}$$ $$\newcommand {\nm }[1]{\left \Vert #1\right \Vert }$$ $$\newcommand {\clo }[1]{\left [#1\right )}$$ $$\newcommand {\ocl }[1]{\left (#1\right ]}$$ $$\newcommand {\rg }[1]{\mathring {#1}}$$ $$\newcommand {\ob }[1]{\overline {#1}}$$ $$\newcommand {\net }[3]{\left (#1_{#2}\right )_{#2\in #3}}$$ $$\newcommand {\qand }{\qquad \text {and}\qquad }$$

# Math 581: Topology 1

Notes by Jerzy Wojciechowski