A generalized Amman's fixed point theorem and its application to Nash equlibrium.
A generalized continuity and product spaces
A generating family for the Freudenthal compactification of a class of rimcompact spaces
For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of and the...
A Hahn-Banach type generalization of the Hyers-Ulam theorem.
A hereditarily normal strongly zero-dimensional space with a subspace of positive dimension and an N-compact space of positive dimension
A Hilbert cube compactification of the function space with the compact-open topology
Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification (X) of C(X) such that the pair ( (X), C(X)) is homeomorphic to (Q, s). In case...
A homological selection theorem implying a division theorem for Q-manifolds
We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward...
A lattice of conditions on topological spaces II
A Lefschetz-type fixed point theorem
A Leray--Schauder alternative for weakly-strongly sequentially continuous weakly compact maps.
A local version of the generalized retract theorem of Ważewski with applications in the theory of partial differential equations of first order
A locally connected non-movable continuum that fails to separate
A Mapping Theorem on Aleph-spaces
A new characterization of compact sets in function spaces
A new characterization of spaces with locally countable -networks
A new hyperspace topology and the study of the function space -
A new semilattice of function algebras and its Boolean form on a lattice of groups.
A new way to find compact zero-dimensional first countable preimages of first countable compact spaces
A nice class extracted from -theory
We study systematically a class of spaces introduced by Sokolov and call them Sokolov spaces. Their importance can be seen from the fact that every Corson compact space is a Sokolov space. We show that every Sokolov space is collectionwise normal, -stable and -monolithic. It is also established that any Sokolov compact space is Fréchet-Urysohn and the space is Lindelöf. We prove that any Sokolov space with a -diagonal has a countable network and obtain some cardinality restrictions on subsets...
A nice subclass of functionally countable spaces
A space is functionally countable if is countable for any continuous function . We will call a space exponentially separable if for any countable family of closed subsets of , there exists a countable set such that whenever and . Every exponentially separable space is functionally countable; we will show that for some nice classes of spaces exponential separability coincides with functional countability. We will also establish that the class of exponentially separable spaces has...