Some mapping theorems for extensional dimension

Some mapping theorems for extensional dimension

We present some results related to theorems of Pasynkov and Torunczyk on the geometry of maps of finite dimensional compacta.

Common Fixed-Point Theorems For Generalized Fuzzy Contraction Mapping

In this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by Gregori and Sapena [V. Gregori, A. Sapena, On xed-point the- orems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252].

Extensional Dimension and Completion of Maps

We prove the following completion theorem for closed maps between metrizable spaces: Let f : X → Y be a closed surjection between metrizable spaces with e-dimf ≤ K, e-dimX ≤ LX and e-dimY ≤ LY for some countable CW -complexes K, LX and LY . Then there exist completions X̃ and Ỹ of X and Y , respectively, and a closed surjection f̃ : X̃ → Ỹ extending f such that e-dimf̃ ≤ K, e-dimX̃ ≤ LX and e-dimỸ ≤...

Some Structure Theorems for

Dimension and Embedding Theorems for Geometric Lattices

Let G be an n-dimensional geometric lattice. Suppose that 1 < e, f < n 1, e + f > n, but e and f are not both n 1. Then, in general, there are E, FE G with dimE=e, dimF=f, EvF=l, and dimEhF=e+f-n-l; any exception can be embedded in an n-dimensional modular geometric lattice M in such a way that joins and dimensions agree in G and M, as do intersections of modular pairs, while each point and lin...