A note about planar completely regular continua with structure

A universal planar completely regular continuum

“…• There is no universal completely regular continuum with structure [1], [6]. • There is no universal element in the class of planar completely regular continua with structure [6].…”

“…We say that K ∈ C is a C-representation of a completely regular continuum X if X is homeomorphic to a subspace of K. The following theorem is proved in [7,Theorem 4.2].…”

“…A completely regular continuum with structure ( K, F , Ã) is said to be universal for a family F of completely regular continua with structure if ( K, F , Ã) ∈ F and for every (K, F, A) ∈ F there exists a homeomorphism h : K → K preserving the structure, that is, h(F ) ⊆ F and h(A) ∈ Ã for every A ∈ A ( [1], [6]).…”