Markov-Kakutani Theorem on Hyperspace of a Banach Space

Markov-Kakutani Theorem and Haar Measure

Hyperspace of a fuzzy quasi-uniform space

The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the c...

On the density of the hyperspace of a metric space

We calculate the density of the hyperspace of a metric space, endowed with the Hausdorff or the locally finite topology. To this end, we introduce suitable generalizations of the notions of totally bounded and compact metric space.

A Theorem on Conjugate Nets in Protective Hyperspace

A theorem proved by C. C. Hsiung in a recent paper [l]1 may be stated as follows : In a linear space Sn of n ( ̂ 3) dimensions let Nx be a conjugate net and w be a fixed hyperplane ; then the points M, M of intersection of the fixed hyperplane w and the two tangents at a point x of the net Nx describe two conjugate nets Nm, Nm in the hyperplane ir, respectively, and one of the two nets Nm, N¡¡ i...

The Brezis-Browder Theorem in a general Banach space

During the 1970s Brezis and Browder presented a now classical characterization of maximal monotonicity of monotone linear relations in reflexive spaces. In this paper, we extend (and refine) their result to a general Banach space. We also provide an affirmative answer to a problem posed by Phelps and Simons. 2010 Mathematics Subject Classification: Primary 47A06, 47H05; Secondary 47B65, 47N10, ...