Minimal Blocking Sets Research Articles

On minimal blocking sets

On minimal blocking sets

Connected projections of blocking sets of 𝐼ⁿ×𝑀

Sufficient conditions are given for each minimal blocking set K of I n × M {I^n} \times M to have the closure of its projection, p ( K ) p(K) , into I n {I^n} connected. The construction of some examples of almost continuous functions f : I n → M f:{I^n} \to M in the literature depends on knowing each p ( K ) ¯ \overline {p(K)} is connected or perfect.

Almost continuous real functions

A blocking set of a function f is a closed set which does not intersect f but which intersects each continuous function with domain the same as f. It is shown that for each function which is not almost continuous, there exists a minimal blocking set. Using this property it is shown that there exists an almost continuous function with domain [0, 1] which is a G δ {G_\delta } set but is not of Baire Class 1, and that there exists an almost continuous function dense in the unit square.