An open-perfect mapping on a hereditarily disconnected space onto a connected space

On the product of a compact space with an hereditarily absolutely countably compact space

We show that the product of a compact, sequential T2 space with an hereditarily absolutely countably compact T3 space is hereditarily absolutely countably compact, and further that the product of a compact T2 space of countable tightness with an hereditarily absolutely countably compact ω-bounded T3 space is hereditarily absolutely countably compact.

Iterative Process for an α- Nonexpansive Mapping and a Mapping Satisfying Condition(C) in a Convex Metric Space

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.

A Hereditarily Indecomposable Asymptotic `2 Banach Space

A famous open problem in functional analysis is whether there exists a Banach space X such that every (bounded linear) operator on X has the form λ+K where λ is a scalar and K denotes a compact operator. This problem is usually called the “scalar-plus-compact” problem [14]. One of the reasons this problem has become so attractive is that by a result of N. Aronszajn and K.T. Smith [7], if a Bana...

A Homogeneous Extremally Disconnected Countably Compact Space

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...

A not on modular hyperconvex space