A generalization of N. Aronszajn's theorem on connectedness of the fixed point set of a compact mapping
A generalization of normal spaces
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
A generalization of Tychonoff's theorem
A generalization of -sets and -sets by means of operators associated with a topology and associated functions.
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 generic theorem in the theory of cardinal invariants of topological spaces
Relative versions of many important theorems on cardinal invariants of topological spaces are formulated and proved on the basis of a general technical result, which provides an algorithm for such proofs. New relative cardinal invariants are defined, and open problems are discussed.
A Geometric Approach to the Bohr Compactification of Cones.
A Hamiltonian property of connected sets in the alternative set theory.
A hedgehog in a product
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 homogeneous space of point-countable but not of countable type
We construct an example of a homogeneous space which is of point-countable but not of countable type. This shows that a result of Pasynkov cannot be generalized from topological groups to homogeneous spaces.
A large -discrete Fréchet space having the Souslin property
A lattice of conditions on topological spaces II
A lemma on finite-dimensional covers
A Lindelöf space X such that is normal but not paracompact
A little more on the product of two pseudocompact spaces
A local-nonglobal Hurewicz fibration
A metrization theorem for countably compact spaces
A minimalization of 0-dimensional metric spaces