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... PROPERTIES OF α -GENERALIZED REGULAR WEAKLY CONTINUOUS FUNCTIONS AND PASTING LEMMA N.SELVANAYAKI AND GNANAMBAL ILANGO ...
... PROPERTIES OF α -GENERALIZED REGULAR WEAKLY CONTINUOUS FUNCTIONS AND PASTING LEMMA N.SELVANAYAKI AND GNANAMBAL ILANGO ...
Some descriptive set theory 1 Polish spaces August 13, 2008
... There are many natural examples of Polish spaces. For example, R is a Polish space under the usual topology and metric because Q ⊆ R is a dense subset. Similarly, [0, 1] is a compact Polish space with the usual metric. Notice that (0, 1) is not a Polish space with the usual metric because the Cauchy ...
... There are many natural examples of Polish spaces. For example, R is a Polish space under the usual topology and metric because Q ⊆ R is a dense subset. Similarly, [0, 1] is a compact Polish space with the usual metric. Notice that (0, 1) is not a Polish space with the usual metric because the Cauchy ...
seminar notes - Andrew.cmu.edu
... Lindelöf (indeed, it is compact; X ∗ is the one-point compactification of the discrete topology on R), but it is not separable since all of the sets {x} remain open for x 6= ∗. ...
... Lindelöf (indeed, it is compact; X ∗ is the one-point compactification of the discrete topology on R), but it is not separable since all of the sets {x} remain open for x 6= ∗. ...
- Bulletin of the Iranian Mathematical Society
... Hausdorff space which contains X as a dense subspace. The Stone–Čech compactification of a completely regular space X, denoted by βX, is the (unique) compactification of X which is characterized among all compactifications of X by the fact that every continuous bounded mapping f : X → F is extendabl ...
... Hausdorff space which contains X as a dense subspace. The Stone–Čech compactification of a completely regular space X, denoted by βX, is the (unique) compactification of X which is characterized among all compactifications of X by the fact that every continuous bounded mapping f : X → F is extendabl ...