Existence of well-filterifications of T0 topological spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

REDUNDANCY OF MULTISET TOPOLOGICAL SPACES

In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^star(U),sqsubseteq)$ and $(Ds(varphi(U)),subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.

σ-Normality of Topological Spaces

Existence of Maximal Elements and Equilibria in Linear Topological Spaces

We present some mathematical theorems which are used to generalize previous results on the existence of maximal elements and of equilibrium. Our main theorem in this paper is a new existence proof for an equilibrium in an abstract economy, which is closely related to a previous result of Borglin-Keiding, and Shafer-Sonneschein, but allows for an i&nite number of commodities and a countably infi...

Nonconstructive Properties of Well-Ordered T2 topological Spaces

We show that none of the following statements is provable in Zermelo-Fraenkel set theory (ZF) answering the corresponding open questions from Brunner in “The axiom of choice in topology”: (i) For every T2 topological space (X, T ) if X is well-ordered, then X has a well-ordered base, (ii) For every T2 topological space (X, T ), if X is well-ordered, then each open cover of X has a well-ordered ...