For an infinite dimensional Banach space, $X^*$ when given the weak* topology is of the first category in itself
106306
$X^*$ with its weak*-topology is of the first category in itself
132491
How to show that $C=C[0,1]$ is a Banach space
128118
Is the cofinite topology on a countable set first countable?
115350
An example of a Banach space isomorphic but not isometric to a dual Banach space
154762
Dual space of a finite dimensional normed space
60692
Is this map to a finite dimensional topological vector space an open map?
63285
Prove that this space is not Banach
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
72190
Topological proof on discrete topology where $X$ is infinite
9295
Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.
77563
Homeomorphism between spaces equipped with cofinite topologies
8314
I am trying to find a Banach Space X and a singular operator (Infinite Dimensional Space)
124458
Quotient of a Banach space $X$ gets quotient topology under standard norm induced from $X$.
46326
The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
154625
$\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
84830
Vector space of infinite sequences in $\Bbb R$