Meromorphic extension spaces

In general topology, one knows several standard extension spaces defined for one class of spaces or another and it is a natural question concerning any two such extensions which are defined for the same space whether they can ever be equal to each other. In the following, this problem will be considered for the Stone-Čech compactification βE of a completely regular non-compact Hausdorff space E[4] and Katětov's maximal Hausdorff extension κE of E[5]. It will be shown that βEκE always holds or, what amounts to the same, that κE can never be compact. As an application of this it will be proved that any completely regular Hausdorff space is dense in some non-compact space in which the Stone-Weierstrass approximation theorem holds.

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Fixed point theory for composite maps on almost dominating extension spaces

Proceedings - Mathematical Sciences ◽

10.1007/bf02829663 ◽

2005 ◽

Vol 115 (3) ◽

pp. 339-345 ◽

Cited By ~ 3

Author(s):

Ravi P. Agarwal ◽

Jong Kyu Kim ◽

Donal O’Regan

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Extension Spaces ◽

Composite Maps

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A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve

International Journal of Mathematics ◽

10.1142/s0129167x14500475 ◽

2014 ◽

Vol 25 (05) ◽

pp. 1450047 ◽

Cited By ~ 4

Author(s):

Insong Choe ◽

G. H. Hitching

Keyword(s):

Moduli Space ◽

Moduli Spaces ◽

Upper Bound ◽

Topological Structure ◽

Vector Bundles ◽

Geometric Interpretation ◽

Maximal Degree ◽

Secant Varieties ◽

Extension Spaces ◽

Orthogonal Case

A symplectic or orthogonal bundle V of rank 2n over a curve has an invariant t(V) which measures the maximal degree of its isotropic subbundles of rank n. This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles. We study this stratification by relating it to another one given by secant varieties in certain extension spaces. We give a sharp upper bound on t(V), which generalizes the classical Nagata bound for ruled surfaces and the Hirschowitz bound for vector bundles, and study the structure of the stratifications on the moduli spaces. In particular, we compute the dimension of each stratum. We give a geometric interpretation of the number of maximal Lagrangian subbundles of a general symplectic bundle, when this is finite. We also observe some interesting features of orthogonal bundles which do not arise for symplectic bundles, essentially due to the richer topological structure of the moduli space in the orthogonal case.

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Local Connectedness Of Extension Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1956-044-8 ◽

1956 ◽

Vol 8 ◽

pp. 395-398 ◽

Cited By ~ 12

Author(s):

Bernhard Banaschewski

Keyword(s):

Topological Space ◽

Dense Subspace ◽

Topological Properties ◽

Local Connectedness ◽

Extension Spaces

1. Introduction. An extension E* of a topological space E (that is, a space containing E as a dense subspace) determines a family of filters (u) on E, given by the traces U ∩ E of the neighbourhoods U ⊆ E* of each u ∈ E* − E. Many topological properties of an extension E* of a given space E can be related to properties of these trace filters (as we shall call them) belonging to E*.

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