Introduction To Topology Mendelson Solutions ^new^

Definition of a metric, open and closed balls, neighborhood systems, convergence of sequences, and continuity via definitions.

Show that the discrete metric ( d(x,y) = 0 ) if ( x=y ), else 1, induces the discrete topology. Introduction To Topology Mendelson Solutions

Let $X$ be a topological space and let $A \subseteq X$. Prove that the closure of $A$, denoted by $\overlineA$, is the smallest closed set containing $A$. Definition of a metric, open and closed balls,

The book is divided into three main sections: Definition of a metric