pseudocompact set
1Pseudocompact space — In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.Conditions for pseudocompactness*Every countably compact space is pseudocompact. For normal… …
2Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …
3Compact space — Compactness redirects here. For the concept in first order logic, see compactness theorem. In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness… …
4Particular point topology — In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and… …
5Topological property — In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space …
6List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …
7Hyperconnected space — In mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two proper closed sets. The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are… …
8Cocountable topology — The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose complement in X is countable. It follows that the only closed subsets are X and the… …
9Feebly compact space — In mathematics, in the realm of topology, a topological space is said to be feebly compact if every locally finite cover by nonempty open sets is finite.Some facts:* Every compact space is feebly compact. * Every feebly compact paracompact space… …
10Ultraconnected space — In mathematics, a topological space X is said to be ultraconnected if no pair of nonempty closed sets of X is disjoint. All ultraconnected spaces are path connected, normal, limit point compact, and pseudocompact.ee also* Hyperconnected… …
