Jager, G. (2016). Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces. Iranian Journal of Fuzzy Systems, 13(3), 95-111. doi: 10.22111/ijfs.2016.2432

Gunther Jager. "Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces". Iranian Journal of Fuzzy Systems, 13, 3, 2016, 95-111. doi: 10.22111/ijfs.2016.2432

Jager, G. (2016). 'Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces', Iranian Journal of Fuzzy Systems, 13(3), pp. 95-111. doi: 10.22111/ijfs.2016.2432

Jager, G. Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces. Iranian Journal of Fuzzy Systems, 2016; 13(3): 95-111. doi: 10.22111/ijfs.2016.2432

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

^{}School of Mechanical Engineering, University of Applied Sciences Stralsund, 18435 Stralsund, Germany

Abstract

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furthermore, we define and study uniform local $mbbe$-connectedness, generalizing a classical definition from the theory of uniform convergence spaces to the lattice-valued case. In particular it is shown that if the underlying lattice is completely distributive, the quotient space of a uniformly locally $mbbe$-connected space and products of locally uniformly $mbbe$-connected spaces are locally uniformly $mbbe$-connected.

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