Higher dimensional cardinal characteristics for sets of functions

Much recent work in cardinal characteristics has focused on generalizing results about ω to uncountable cardinals by studying analogues of classical the generalized Baire and Cantor spaces κ 2 . In this note I look at generalizations other function spaces, focusing particularly space functions f : → By considering invariants setting derive a number “higher dimensional” such cardinals, ultimately introducing 18 new invariants, alongside framework that allows for numerous others. These form two separate diagrams consisting 6 12 respectively, each resembling versions Cichoń diagram. ZFC -inequalities are first main result paper. then consider relations between these as well c + show rely additional assumptions Finally, using variations Cohen, Hechler, localization forcing prove consistency possible values cardinals.