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On the ΄΄Fragmentation΄΄ of Certain Pseydocompact Groups

W. W. Comfort — 1984

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues

W. W. Comfort — 1968

Fundamenta Mathematicae

Functions linearly continuous on a product of Baire spaces.

W. W. Comfort — 1965

Bollettino dell'Unione Matematica Italiana

Compact-covering numbers

George Baloglou; W. Comfort — 1988

Fundamenta Mathematicae

Imposing psendocompact group topologies on Abeliau groups

W. Comfort; I. Remus — 1993

Fundamenta Mathematicae

The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, $m (α) \leq 2^{α}$ . We show: Theorem 4.12. Let G be Abelian with |G| = γ. If either m(α) ≤ α and m $(α) \leq r_{0} (G) \leq γ \leq 2^{α}$ , or α > ω and $α^{ω} \leq r_{0} (G) \leq 2^{α}$ , then G admits a pseudocompact group topology of weight α. Theorem 4.15. Every connected, pseudocompact Abelian group G with wG = α ≥ ω satisfies $r_{0} (G) \geq m (α)$ . Theorem 5.2(b). If G is divisible Abelian with $2^{r_{0} (G)} \leq γ$ , then G admits at most $2^{γ}$ -many...

Extending continuous functions on X x Y to subsets of βX x βY

W. Comfort; Stelios Negrepontis — 1966

Fundamenta Mathematicae

Topologies induced by groups of characters

W. Comfort; K. Ross — 1964

Fundamenta Mathematicae

Some topological properties associated with measurable cardinals

W. Comfort; S. Negrepontis — 1970

Fundamenta Mathematicae

On families of large oscillation

W. Comfort; S. Negrepontis — 1972

Fundamenta Mathematicae

Extremal phenomena in certain classes of totally bounded groups

W. W. Comfort; Lewis C. Robertson — 1988

For various pairs of topological properties such that P ⇒ Q, we consider two questions: (A) Does every topological group topology with P extend properly to a topological group topology with Q, and (B) must a topological group with P have a proper dense subgroup with Q? We obtain negative results and positive results. Principal among the latter is the statement that any pseudocompact group G of uncountable weight which satisfies any of the following three conditions has both a strictly finer pseudocompact...

Cardinal invariants for κ-box products: weight, density character and Suslin number

W. W. Comfort; Ivan S. Gotchev — 2016

The symbol ${(X_{I})}_{κ}$ (with κ ≥ ω) denotes the space $X_{I} : = \prod_{i \in I} X_{i}$ with the κ-box topology; this has as base all sets of the form $U = \prod_{i \in I} U_{i}$ with $U_{i}$ open in $X_{i}$ and with $| i \in I : U_{i} \neq X_{i} | < κ$ . The symbols w, d and S denote respectively the weight, density character and Suslin number. Generalizing familiar classical results, the authors show inter alia: Theorem 3.1.10(b). If κ ≤ α⁺, |I| = α and each $X_{i}$ contains the discrete space 0,1 and satisfies $w (X_{i}) \leq α$ , then $w (X_{κ}) = α^{< κ}$ . Theorem 4.3.2. If $ω \leq κ \leq | I | \leq 2^{α}$ and $X = {(D (α))}^{I}$ with D(α) discrete, |D(α)| = α, then $d ({(X_{I})}_{κ}) = α^{< κ}$ . Corollaries 5.2.32(a) and...

Some recent applications of ultrafilters to topology

Comfort, W. W. — 1977

General topology and its relations to modern analysis and algebra IV

Locally compact realcompactifications

Comfort, W. W. — 1967

General Topology and its Relations to Modern Analysis and Algebra

Correction to the paper “The Bohr compactification, modulo a metrizable subgroup” (Fund. Math. 143 (1993), 119–136)

W. Comfort; F. Trigos-Arrieta; Ta-Sun Wu — 1997

Fundamenta Mathematicae

The Bohr compactification, modulo a metrizable subgroup

W. Comfort; F. Trigos-Arrieta; S. Wu — 1993

Fundamenta Mathematicae

The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can hold for suitable...