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We prove the indecomposability of the Galois representation restricted to the $p$-decomposition group attached to a non CM nearly $p$-ordinary weight two Hilbert modular form over a totally real field $F$ under the assumption that either the degree of $F$ over $\mathbb{Q}$ is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of $F$.

The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...

We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A $T_0$ space $(X,\tau )$ is a quasicontinuous space if and only if $SI\left(X\right)$ is locally hypercompact if and only if $({\tau }_{SI},\subseteq )$ is a hypercontinuous lattice; (2) a $T_0$ space $X$ is an $SI$-continuous space if and only if $X$ is a meet continuous and quasicontinuous space; (3) if a $C$-space $X$ is a well-filtered poset under its specialization order, then $X$ is a quasicontinuous space...