real analysis - assume h:R->R is continous on R and let K={x:h(x)=0}. show that K is a closed set.

real analysis - show that a set E is nowhere-dense in R if and only if the complement of E Clouser(E on top bar) is dense in R.

Closure - Prove: If H and K are disjoint closed point sets, then there exist open point sets U and V containing H and K respectively such that cl(U) and cl(V) are disjoint.

real analysis.7 - Give formal negations of the following definitions: * Limit point. Your answer should be in the form: "A point p in X is NOT a limit point of the set E in X if ... " * Interior point. Your answer should be in the form: "A point p in X is NOT an interior point of the set E in X if ... " * Closed set. Your answer should be in the form: "A set E in X is NOT closed i...

real analysis - if {G1,G2,G3,...} is a countable collection of dense, open sets then the intersection(U top infinity bottom n=1)G_n is not empty.