Connectedness and compactness in \(C(X)\) with the \(m\)-topology and generalized \(m\)-topology

DOI10.1016/j.topol.2012.08.010zbMath1255.54009OpenAlexW2025360817MaRDI QIDQ714755

F. Manshoor, F. Azarpanah, Rostam Mohamadian

Publication date: 11 October 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2012.08.010

zbMATH Keywords

componenthemicompact\(m\)-topologygeneralized \(m\)-topologyquasicomponenttotally disconnected and hyper-real maximal ideal

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Algebraic properties of function spaces in general topology (54C40)

Related Items (11)

The largest topological ring of functions endowed with the m-topology ⋮ A generalization of topology of uniform convergence on \(C(X)\) ⋮ Clopen linear subspaces and connectedness in function spaces ⋮ Unnamed Item ⋮ Strong Whitney and strong uniform convergences on a bornology ⋮ A generalization of the m-topology on C(X) finer than the m-topology ⋮ Compactness, connectedness and countability properties of \(C(X)\) with the \(r\)-topology ⋮ On subrings of the form \(I+\mathbb{R}\) of \(C(X)\) ⋮ Unnamed Item ⋮ Connectedness of ordered rings of fractions of C(X) with the m-topology ⋮ m-TOPOLOGY ON THE RING OF REAL-MEASURABLE FUNCTIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topologies on the space of continuous functions
• Nonnormality or hereditary paracompactness of some spaces of real functions
• The \(m\)-topology on \(C_{m}(x)\) revisited
• Stone-Čech compactification of a product
• Intersection of essential ideals in $C(X)$
• Functions with pseudocompact support
• Supports of Continuous Functions
• Rings of Real-Valued Continuous Functions. I

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