Previous Page 3

Displaying 41 – 47 of 47

Showing per page

An interesting class of ideals in subalgebras of C ( X ) containing C * ( X )

Sudip Kumar Acharyya, Dibyendu De (2007)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we give a duality between a special type of ideals of subalgebras of C ( X ) containing C * ( X ) and z -filters of β X by generalization of the notion z -ideal of C ( X ) . We also use it to establish some intersecting properties of prime ideals lying between C * ( X ) and C ( X ) . For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime.

Approximation theorems for compactifications

Kotaro Mine (2011)

Colloquium Mathematicae

We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of n + 1 . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder...

Currently displaying 41 – 47 of 47

Previous Page 3