The projection methods in countably normed spaces

On the Radial Projection in Normed Spaces

Our concern is with the Lipschitz constant of T; i.e. with the constant K such that || J # — 7 j | | ^i£||#—;y|| for all x, y in X. In particular, we wish to determine under what conditions on the space X the mapping T will be nonexpansive, i.e. K = l. T is a special case of a proximity mapping defined by a convex set in a normed vector space, i.e. a mapping which assigns to each point of X, th...

Countably I-compact Spaces

We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other chara...

Separation in Countably Paracompact Spaces

We study the question "Are discrete families of points separated in countably paracompact spaces?" in the class of first countable spaces and the class of separable spaces. Two of the main directions of research in general topology in the last thirty years have been the work of Jones, Bing, Tall, Fleissner, Nyikos and others motivated by the normal Moore space problem (when are discrete familie...

-approximation in normed spaces

On Σ-countably Tight Spaces

Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality c if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and σ-countably tight compactum has cardinality c remains open. We also show that if an arbitrary product is σ-countably tight then all but finitel...